NEW YORK — Back and forth across the country Frank Swann flew for months this spring and summer, dusting off all the dormant “Hamiltons”: a “Hamilton” due to restart in Los Angeles, another “Hamilton” in Tempe, Ariz., a “Hamilton” in Atlanta and a “Hamilton” in San Francisco. Sets for these touring and sitting productions had to be retrieved from warehouses and storage trucks; backstage motors and wheels and audio equipment had to be retested and fixed.

And costumes for actors playing all of those Thomas Jeffersons and George Washingtons and Eliza Schuylers had to be spruced up and in some cases refitted. Because, you know, some girth may have been acquired (or shed) in the year-and-a-half-long absence of all that acting and singing.

“It was a little bit like ‘Groundhog Day,’ like reliving the same week over and over again,” Swann, a lead production supervisor, said of the national, multi-“Hamilton” restoration effort. We spoke recently at Swann’s Times Square office at Hudson Scenic Studio, one of Broadway’s key behind-the-scenes companies. Heck, the company is so essential there wouldn’t be scenes without it.

The return of live theater, particularly Broadway and its touring incarnations, requires a mobilization unparalleled in history; Broadway shows stopped dead in their tracks in March 2020, when the pandemic shut down the performing arts. The production teams simply had to hurriedly depart their stages with scenery still in place, costumes hanging on racks and dressing rooms abandoned — leaving behind a kind of theatrical Pompeii.

“We literally got up and left,” recalled Neil A. Mazzella, the lavishly maned chief executive of Hudson Scenic Studio, the 40-year-old company that fabricates sets for dozens of musicals and plays in its Yonkers workshop. (The company, which employs as many as 100 workers, also takes care of the automation of scenery and stays with shows to maintain their technical aspects.)

Now imagine the immensity of the task of snapping this entire industry, which pumps about $15 billion a year into the New York City economy, out of its suspended animation all at once — with Hudson as one of the go-to outfits for Broadway’s wake-up call.

Every time you turn around in Times Square this fall, another box office has reopened for business, another marquee is emblazoned with the obvious subtext: We are here! That bustle is why Mazzella and his five lead production supervisors are so consumed. Every show they have worked on has had to be tended to, and almost all at once, to prepare for rebirths. A few shows have been lost to the pandemic, including “Hangmen,” a play by Martin McDonagh that was to have had a spring 2020 run. With the production scuttled, its sets were sent to the landfill.

For every “Hangmen,” though, there is a robust line of enterprises that have made or are awaiting their Hudson-assisted entrances: such Broadway warhorses as “The Lion King” and “Chicago”; newcomers “Chicken & Biscuits” and “Mrs. Doubtfire”; tours of Tony winners, including the 2019 revival of “Oklahoma!” and the 2019 best musical, “Hadestown,” now at the Kennedy Center.

Each of Mazzella’s lieutenants has three or four shows to stay on top of, each consulting a seemingly endless checklist of tasks to be finished, some common to all productions, some unique to the artistry of a given project. Everywhere, the air purifiers and scrubbers — critical in the covid age to maintaining healthy air flow — must be cleaned; the dozens of hoist motors that fly the scenery must be checked and, if need be, replaced; and curtains and other potential fire hazards are re-treated with flame retardant and readied for fire department recertification.

“You gotta keep jumpin’,” said Sam Ellis, a Hudson veteran who is responsible for three returning Broadway shows, “Girl From the North Country,” “Jagged Little Pill” and “Ain’t Too Proud: The Life and Times of the Temptations.” On a recent morning, Ellis was at the storied Belasco Theatre on West 44th Street, where a crew was working around the actors arriving for a rehearsal of “Girl From the North Country,” which restarted Oct. 13.

Tagging along with Ellis provided a true nuts-and-bolts portrait of backstage life in the theater, because he’s in charge of the nuts and bolts. And loving this world is a requirement to be in Mazzella’s employ.

“If you want to be with me, you have to be a theater person,” said Mazzella, a Yale Drama School grad so well thought of that he has just been awarded the Yale Medal, the highest honor bestowed by the university’s alumni association. “You have to be engaged.”

A truism of the physical world plays out in all the nooks and crannies of a theater: Things fall apart. The natural deterioration of machinery and material in a playhouse in which upkeep had basically ceased leads to damaged wiring and moth holes in costumes, among other problems.

“We had to schedule dry-cleaning like we never had to before,” Mazzella said. Leaks have been discovered in some theaters; issues peculiar to putting on a show have cropped up in others.

“In the fog system of ‘Hadestown,’ we found mold,” Mazzella said, in the “Hey, no biggie” tone of a guy who has troubleshot everything. “We had to change all the hosing.”

Some Broadway houses are more than a century old, but all of them, regardless of age, are workplaces, and making the environment hazard free for actors and stagehands is a topmost concern. At the Belasco, Ellis led a tour into the belly of the theater, a cavernous basement used by the actors as a green room but known more legendarily as the “Elephant Room.” Ellis explained where that name came from: Once upon a time, magician Harry Houdini performed an illusion with a real elephant that required it to “disappear” by being lowered through a trap door in the stage and into the basement below.

The elephant is long gone, but the job of maintaining a healthily operating backstage is forever. “The cast wants to know what we’ve done to make it safe,” Mazzella said. “That means cleaning it and keeping it clean top to bottom.”

At the St. James Theatre, where “American Utopia,” the David Byrne theatrical concert, has reopened, the ongoing upkeep issue is more exotic. The set consists of hundreds of metal chains hanging 27 feet high around three quarters of the stage. On a recent morning, Mazzella greeted stagehand Timmy McDonough, who was brandishing a garden rake to comb out kinks in the chains. It seemed a painstaking task.

“They break off all the time,” McDonough said. “It’s a lot of chains, but it has to look perfect.”

So it goes in this season of renewal, of touching up scenery and replacing casters on turntables. Mazzella made a stop at the Stephen Sondheim Theatre on West 43rd Street to see how work was progressing on “Mrs. Doubtfire.” One of the few new musicals this fall, it was just getting on its feet in March 2020, when the pandemic brought down the curtain. Its second life began with a preview on Oct. 21. But before that, an order had come in to Hudson to redo one of the sets. So he had a crew of painters and carpenters onstage, adding what he said was “more detail in than your own apartment.”

With so much riding on completing all these jobs, one might think the head of Hudson would be a nervous wreck. But this is one chill maestro of the hoists and winches.

“I don’t believe in stress,” Mazzella said.

“I don’t go with the highs. I don’t go with the lows. I have been there for ‘Hamilton’ and for ‘Moose Murders,’ ” he added, referring to one famous hit and one infamous flop. “You just have to stay balanced.”

Correction: An earlier version of this story misspelled Frank Swann’s last name. The story has been updated.