TAMPA, Fla. — Whether it’s Broadway or Hempstead Turnpike or Flatbush Avenue, Jon Cooper understands this: Winning in New York means something.

The Lightning coach, in his fourth season behind the bench, was thrilled when his team beat the Rangers at Madison Square Garden last spring in Game 7 of the Eastern Conference finals.

And the former lacrosse midfielder, who played at Hofstra in the late 1980s, will be back in the city next week when the Lightning, which trails the Islanders 1-0 in the best-of-seven second-round series, visits Barclays Center in Brooklyn for Games 3 and 4.

After Thursday’s practice at Amalie Arena, Cooper, 48, took a minute to reflect on the upcoming trip — and the New York hockey venues past and present — in what is another high-stakes matchup.

The Lightning has played at Barclays only once: On April 4, the Islanders prevailed, 5-2. The other two games were in Florida.

Said Cooper, “It’s a different arena than the Coliseum. It’s the luxury arena versus the enclosed, intimate, rowdy scene that the Nassau Coliseum was, but ultimately, the fans are still pretty much the same. They still do their chants, they still do their goal celebrations, they still get into it.”

He then referenced the “Potvin [stinks]” taunt that still surfaces at the Garden.

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“Denis is going to kill me for that,” Cooper said with grin, “but it’s New York, the fans are passionate up there. Just going through the experience last year [against the Rangers], it was unreal. I don’t expect any of that will change because you’re going across the bridge.”

Steve Buck, a suitemate of Cooper’s at Hofstra, said Thursday that Cooper certainly will be pumped up for Brooklyn and the playoffs even though the venue is not the Coliseum. As undergrads, they’d walk across the street and watch players such as Brad Lauer, now a Tampa Bay assistant coach, Derek King, Mick Vukota, Pat LaFontaine and yes, Potvin, now a Panthers announcer.

Like most hockey coaches, Cooper worked his way up the ladder: a Junior B team in Michigan, the North American League’s Texarkana Bandits, the Green Bay Gamblers of the USHL, and the AHL’s Norfolk Admirals and Syracuse Crunch, a Lightning affiliate.

“Coop always looks at coming to New York as playing at the highest professional level,” Buck said. “And every year it’s [the playoffs] more and more intense. I don’t think moving from the Coliseum to Brooklyn is a big difference; you’ve got Islanders fans still going to follow the team.”

But before Cooper returns to the metropolitan area, there is unfinished business here. “We have lost Game 1 in previous series, both at home and on the road, and came back,” he said. “It makes Game 2 [Saturday] paramount. Not that the series is over, but you continue to make it harder on yourselves.”

Compared to playing the Detroit Red Wings in the first round, Cooper said this series is “two teams who haven’t played each other that often, are not in the division, and [Game 1] had a little different feel to it. I’m sure when the Islanders play the Rangers, it’d be much different than them playing the Lightning. But that’s how rivalries grow. ”