PIZZA is to Italy what french fries are to France, peasant food gone off to the new world to become rich and famous.

In the process it's been adopted as native and turned so modern that its old home town might not recognize it. Cheap, highly spiced and portable, pizza is--ask anybody--classic American food.

Some people crave the flat, chewy old-fashioned version, once called Neapolitan and now Americanized as New York pizza. Others say it's not pizza at all unless it is an inch thick, either flat-baked Sicilian or the Chicago style, baked in a deep, dark pan with a ton of topping. In between, there are rectangular pizzas, white pizzas and, relatively new attractions, double-crust and nouvelle pizzas. Some people judge a pizza by its crust, others say the sauce reflects overall quality and some say the cheese is the only criterion that matters.

In any case, pizzas differ within their genre, and in every case, nobody feels indifferent about them.

"Pizza lovers tend to be die-hards," says Allen Kelson, editor-in-chief of Chicago magazine. "There's no gray area. Either pizzas are great or they're terrible."

There is no consensus on who has the best.

"Chicago's kind of the capital of the pizza business," concedes New York food writer Calvin Trillin, author of what he calls his "tummy trilogy": "American Fried," "Alice Let's Eat" and the about-to-be-released "Third Helpings." One could say, however, that a displaced Kansas boy like Trillin might not know from Naples.

Mike Losurdo, who's distributed pizza fixings up and down the East Coast for 25 years, counters, "Midwestern pizza is a figment of the American imagination." Real pizza, he says, is Neapolitan style--thin crust, simple sauce and fresh whole-milk mozzarella.

"The key word is simplicity," says Losurdo. You take your basic bread dough, let it rise once and "open it up by hand" (no rolling, he insists). Then top it with crushed tomatoes, a little oregano, romano cheese, salt and pepper and some mozzarella, then "bake it off until the bottom is nice and brown." Losurdo's favorite pizza is in any one of a half dozen or so pizza parlors in northern New Jersey and New York.

Peter Castellotti, of John's Pizzeria in Greenwich Village, reiterates that New York pizza has thin crust. His dough is worked by hand on marble, and the 1/4-inch-thick crust is put into coal-burning ovens.

Cheese is the topping requested by 85 percent of the New York pizza eaters, according to Larry Goldberg of Goldberg's Pizzeria in New York. "New Yorkers are very obsessed with cheese. They like pizza thin with a lot of cheese."

Still, says Goldberg, the "most serious pizza town is Chicago. People grab a slice and run down the street in New York." In Chicago, pizza "is real serious dining out."

"Chicagoans are kind of crazy about indigenous foods," says Chicago magazine's Kelson. "We were all weaned on this stuff. Chicago is not a prissy town."

So Chicagoans dig deep for their pizza; deep into a heavy black pan that absorbs the heat and keeps the thick crust crunchy. The deep dish holds the fat, anathema to Italian cooks. But in Chicago, it makes the pizza crust short, like pie crust. It even crunches. "It's almost french fries," says Kelson. The sauce is deep, but the crust can support it, and there's a lot of cheese.

In addition, Chicagoans like their toppings. Goldberg says he can tell when midwesterners order pizza in his New York parlor because they request toppings. Kelson says the big topping in Chicago is sausage. Actually, any combination is fine, says Kelson, but it has to go on dry. With so much topping, "sogginess really makes its presence known."

The newest thing in Chicago is double-crust pizza, a kind of calzone-in-a-pan. True to its name, the pizza has conventional pizza-dough crust on the bottom and the top. Toppings have become innards and are more unconventional than even Chicagoans are accustomed to. Kelson guesses that spinach and mushroom is the big double-crust combo, and he insists that the 2 1/2-by-5-inch pie is a meal for one.

In either town, homemade pizza may seem a contradiction in terms--Larry Goldberg says eating out is part of the pizza experience--but there are some people who can pull it off.

Calvin Trillin's wife, Alice, mixes a crust of semolina flour, lets it rise only 20 minutes and rolls it "really, really thin . . . which I love," she says. She puts the thin crust on a preheated stone and cooks it part way, then flips the crust, tops it with sliced fresh tomatoes, salt, pepper and thyme and bakes it again. The crust comes out cracker-like, "incredibly crisp," says Alice. "A really bizarre pizza."

Bizarre is in the eye of the beholder, perhaps. White pizza may appear strange to some, but it's only basic pizza crust with a little seasoning, at its best with just a rubbing of olive oil and salt. Tradition also encompasses a shake of red pepper, and maybe some oregano. And elaboration has taken over to sprinkle cheese over the herbs and oils, even cheese combinations.

Whether nouvelle or old world, all pizzas are only variations on a theme. In the beginning, leftover bread dough was stretched thinly and topped with whatever was handy and it was homemade. It still can be. LEE'S PIZZA (2 14-inch round pizzas) Crust: 1 package dry yeast 2 tablespoons vegetable oil 2 teaspoons salt 2 tablespoons sugar 1 cup hot milk 3 cups whole-wheat flour 3 cups white flour Sauce: 29 ounce can tomato sauce 1 1/2 teaspoons oregano 1 tablespoon minced parsley 1 teaspoon minced garlic 1/2 teaspoon basil 1/2 teaspoon rosemary Toppings: 3/4 pound cooked, drained sausage pieces; 2 medium onions, sliced; 1 green pepper, chopped and/or 3/4 pound hamburger, browned and drained 1 1/4 pounds grated mozzarella cheese

Dissolve yeast in 1/4 cup warm water. While this is standing, combine oil, salt and sugar in bowl. Add hot milk and 1 cup hot water. Add 1 1/2 cups whole-wheat flour and 1 1/2 cups white flour and mix until blended. Add yeast mixture and blend again. Add 1 1/4 cups whole-wheat flour and 1 1/4 cups white flour and combine well. Knead on floured board 8 to 10 minutes, adding last 1/2 cup of flour as needed, until dough has smooth, elastic texture. Put dough in greased bowl and let rise in warm place 1 hour.

Divide in half and spread evenly on 2 greased 14-inch pans. Let rise again 20 to 30 minutes.

Combine sauce ingredients. Spread on pizzas. Sprinkle with topping suggestions (or make up a few of your own) and then sprinkle evenly with mozzarella cheese. Bake at 425 degrees for 25 minutes or until cheese is browned. WHITE PIZZA FORMAGGIO (2 14-inch round pizzas) 1 package active dry yeast 1 teaspoon sugar 1 3/4 cups warm water 5 cups unbleached flour (approximately) 4 to 6 tablespoons olive oil Red pepper flakes Oregano 5 to 6 cloves garlic (or to taste), minced 8 ounces mozzarella cheese 2 to 4 ounces freshly grated parmesan cheese

Combine yeast, sugar and water in a medium bowl. Add flour and blend well. Turn onto floured surface and knead about 10 minutes, adding flour as necessary. The dough should be firm, not sticky, but still very soft and easy to work with. Replace in bowl and set aside for 20 minutes or so.

Punch dough down. Oil 2 14-inch round pizza pans. Using your fingertips, press half the dough out from the center to the sides of one of the pans. It should be about 1/4-inch thick. Rub the dough with half the olive oil, then sprinkle with red pepper flakes, oregano and half the garlic. Sprinkle with half the cheese. Repeat for another pizza. Bake at 450 degrees for 10 to 12 minutes, until cheese is melted, bubbling and brown. Slice and remove from pan to racks. Serve immediately. DOUBLE-CRUST PIZZA (6 servings)

This pizza crust is crunchy and cracker-like. Substitute your favorite tomato sauce for the pure'ed tomatoes, if desired. For a traditional, chewy pizza crust, substitute unbleached flour for the semolina. 2 packages active dry yeast 1 teaspoon sugar 3/4 cup hot water 1/2 teaspoon salt 3 to 4 cups semolina flour 1/2 cup olive oil 1 pound ricotta cheese 1/4 teaspoon grated nutmeg 1 pound fresh spinach 4 to 8 ounces grated provolone cheese 1/2 pound mushrooms, sliced Salt and freshly ground pepper 1 medium onion, sliced and separated into rings 1 1/2 cups peeled, sliced tomatoes (well drained) 1 teaspoon fennel seeds 1 egg yolk

Combine yeast, sugar and water and set aside for about 10 minutes. Mix 3 cups of flour with 1/2 teaspoon salt. Add 5 tablespoons olive oil and blend well. Place dough on a floured board and knead, adding extra flour as necessary, to get a smooth but not sticky ball (about 10 minutes). This process takes just a minute or so in the food processor. Cover and set aside. (This dough does not feel springy the way dough made with regular flour would.)

Place ricotta cheese and nutmeg in a bowl. Wash spinach, trim stems and discard. Chop the leaves and place in a dry skillet. Cover and steam over low heat until the spinach is wilted (do not add water), stirring occasionally. After the spinach has wilted, remove the top to evaporate any moisture. The spinach should be quite dry. Add to ricotta cheese. Stir in half the provolone.

In the same skillet, heat remaining 3 tablespoons of olive oil. Add mushrooms and cook until they give up their liquid and it has evaporated. Salt and pepper to taste. Slice the onions. Put the well-drained tomatoes through a food mill to make pure'e. Add a lot of freshly ground pepper, the fennel seeds and salt as desired.

Halve the dough. Lightly oil a 14-inch pizza pan. With a rolling pin, roll the dough to fit the pan; it should be very thin and delicate but not sticky. Place in pizza pan. Cover this with spinach and cheese mixture, then mushrooms. Pour tomato sauce over these and distribute onions over the top. Cover with remaining grated cheese. Roll out remaining dough and place this layer over the stuffing. Press the edges of the two layers so they adhere. Brush the top with egg yolk beaten with a little water. Bake at 400 degrees for 15 minutes, then reduce heat to 375 and bake 20 minutes more.