In Texas, Republican congressional candidate Jim Bradshaw, peddling the president's programs, jokingly likens himself to the sales manager for Tylenol, while in rural Kansas, Democratic candidate Jim Slattery distributes a brochure that does not mention party identification.

In Missouri, black Democrat Alan Wheat proudly displays a high rating from the local chamber of commerce, while in Pennsylvania, Republican Tom Ridge is trying to hold onto blue-collar Democrats who voted for President Reagan in 1980.

What binds together these and 112 other disparate candidates for Congress is that they are combatants in perhaps the most intensely fought battle in the 1982 midterm election, the battle for the 58 open seats where there is no incumbent running for reelection.

The battleground stretches from the cactus-covered desert of southern Arizona to the factories of western Connecticut, from the ranches of eastern Oregon to the palaces of Palm Beach. But volatility, not geography, makes the landscape significant.

If history is any guide, a greater percentage of these districts will switch parties than in races involving incumbents. Over the last decade, about 25 percent of the open seats have changed affiliation, compared to less than 10 percent of seats held by incumbents.

Party officials and independent analysts estimate that about 23 of the 58 are now highly competitive. Of the remaining 35, the Democrats are given an edge in 23, the Republicans in 12.

For the Democrats, open seats offer opportunities to use the economy to make quick gains without having to topple an entrenched Republican incumbent. For the Republicans, they offer chances to overcome the political liability of 10.1 percent unemployment with money and technical assistance.

"If you look at the midterm elections for what they will tell you, the open seats represent the clearest test of party," said Ann Lewis, political director for the Democratic National Committee.

There is one caveat, however. If 1982 turns into a Democrat landslide, as some public opinion polls suggest, it will show up most clearly in races involving incumbent Republicans, simply because there are so many more contests that feature incumbents.

The number of open seats this year is somewhat above the average of the last decade. What makes this year unusual is not the numbers involved, but the fact that more than one-third of the seats are wholly new districts created through reapportionment.

Of the 58 open seats, 21 were held by Democrats in the 97th Congress, and 16 by Republicans. The remaining 21 are the newly drawn districts that one Republican describes as "prizes for anyone who gets there first."

In all those numbers, Republicans see hope. "We only have to protect 16 seats," says Nancy Sinnott, executive director of the National Republican Congressional Committee. "All the others are possible gains for us."

That is important at a time when Republicans are increasingly nervous about the potential for sweeping Democratic gains. The GOP has been pouring money into television advertising, direct mail and phone banks in these districts to stem their losses.

Running in an open district is expensive. In 1980, for example, the average expenditure of candidates in open seats was $209,393. By comparison, incumbents seeking reelection that year spent an average of $165,502, while challengers to incumbents spent just $128,293.

"It's not surprising you have party switches [in open seats] because you have real contests there," said Thomas E. Mann, co-author of "Vital Statistics on Congress, 1982," published by the American Enterprise Institute, from which the figures are drawn.

So far, the Republicans' financial advantage seems to be paying off. A combination of voter ambivalence toward both parties and GOP money has kept many of these races close at a time when, many party officials agree, the election may be sliding toward the Democrats. The Republican party has contributed the maximum allowed by law, about $35,000, in nearly every open district in the country, certainly in every one it considers competitive. The Democrats have given about $5,000 to a much shorter list of candidates.

"The same people who gave unemployment to the middle class, the same people who gave cheese lines to the poor, now think that by pouring money into this congressional race, they can buy our next congressman," state Sen. Anthony (Buzz) Andrezeski, who is running against Tom Ridge in northwest Pennsylvania, recently told a union audience.

Because the candidates in open seats do not have their own records to run against and because their ties to national party policies are more tenuous, the political debates in these districts may offer the sharpest mirror of political attitudes around the country this fall. What emerges from listening to almost a dozen candidates is a desire by both parties to shift back toward the center.

Thus, in Kansas, Republican Morris Kay defends Reagan, except on defense spending, while in Arizona, Republican Jim Kolbe worries about the Reagan program's fairness.

Kolbe's opponent, Democrat Jim McNulty, runs against the president's economic program, but said, "We're not talking about going back to the spending of the past. There is a middle way."

But many of these races ultimately will turn on personality, which is why Pennsylvania's Tom Ridge feels optimistic.

"If people think that Reagan did something wrong," he said in a hopeful tone of voice the other day, "that doesn't necessarily translate to me."