NEW YORK – John Tortorella took the New York Rangers to the second round of the Stanley Cup playoffs. Four days after their ouster, the blustery coach was on the outs, too.

Alain Vigneault owns more victories behind the Vancouver bench than any other coach (313), yet that wasn’t enough for him to keep his job, either, after seven seasons with the Canucks.

In an odd twist, Tortorella and Vigneault have swapped jobs and will look to improve where their predecessor could not. The NHL regular season starts Tuesday.

An American coach in Vancouver. A Canadian coach in New York. Maybe that is the recipe for these franchises that met in the 1994 Stanley Cup Final — with the Rangers winning in seven games — and combined for one appearance since.

“I really want everybody to come in with a clean slate,” Vigneault said at the opening of his first Rangers training camp. “I don’t want to come in with any preconceived notion. I want guys to have a legitimate chance.”

That included putting the message on T-shirts: “Clean slate … Grab It.”

Direct and to the point, but that is likely where similarities between Vigneault and Tortorella end.

Whether Tortorella’s loud voice had been tuned out by the Rangers by the time they were eliminated by Boston is debatable, but general manager Glen Sather got a clear indication a change was needed after exit interviews with players.

“I loved working there,” Tortorella said of New York. “Did I want to leave? No. I was told to leave, and I left. It’s part of the game. I’m knee-deep in it here, trying to get this team ready to play.”

While Vigneault’s tone is much less abrasive than Tortorella’s, his approach and message seemed to have grown tired, too, in Vancouver.

The Canucks were eliminated in the first round of the playoffs after each of the last two seasons.

“When you meet players, sometimes (they say), ‘Oh, I know I can do more, and I know I can do this,’ ” said Vigneault, 52. “Well, let them have the opportunity to show me and the rest of management and the rest of the coaching staff.”

Tortorella, 55, might be looking for a bit of a clean slate himself. He takes over a Canadian team for the first time in his coaching tenure that includes a Stanley Cup title with the Tampa Bay Lightning in 2004.

On the day he was introduced in Vancouver, Tortorella recognized his infamous temper has caused him trouble.

“This is the mess I put myself into, and this is the mess I’m going to get myself out of,” Tortorella said. “When you lose your job, you crawl into a hole a little bit, you reassess yourself, you try to learn. I have certainly gone through that process.

“Have I made mistakes? Absolutely. I make my own bed in this type of situation with the perception of myself in the media.”

If both men can win in their new jobs, any flaws or faults will become quieter conversation pieces.

“I don’t think changing the culture of a team happens overnight,” Tortorella said.

The Rangers and Canucks will meet Nov. 30 in New York and April 1 in Vancouver.

“I do know that Alain did a hell of a job here,” Tortorella said.

Get set for the Canucks to sport various bumps and bruises as they learn to get more aggressive, put themselves into opponents’ shooting lanes and face the related danger of that tactic.

“It’s coming along,” Tortorella said. “There are habits one way, and we’d like to try it another way that we’ll continue to work at.”

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