The Mets and Yankees play their first Subway Series games of this season at Citi Field starting on Tuesday night, a few days before the 26th anniversary of the first Interleague game between the two teams at the old Yankee Stadium on June 16, 1997. A Met journeyman named Dave Mlicki shocked himself and the world by throwing a complete-game shutout that night, and a rivalry that had existed only in the imaginations of New York baseball fans was finally joined in a game that counted.

But understand: Nobody in New York has ever thought of it as Interleague baseball. This was something a lot deeper in the city, something that reached all the way back across baseball’s 20th century to the '20s, after Babe Ruth got with the Yankees and they played three World Series in that decade against the old New York Giants. That was before the Yankees and the Brooklyn Dodgers would play six Subway Series against each other in the '40s and '50s, as rich a part of baseball history as there is in any city.

• Most memorable Subway Series moments

In New York, this has always been about interborough baseball, and why it has felt important every single time the two teams have played since ’97.

It is why, for a handful of nights every season, this always feels and sounds as important a rivalry as either team has, even if the seasons the Mets and Yankees are playing right now aren’t the ones for which their fans signed up, the Mets especially.

If you have ever attended one of these games, and I’ve attended a lot of them since ‘97, if you’ve ever been there at the old Stadium or the new Stadium or Shea Stadium or Citi Field, you know what it’s been like. You certainly know what it was like at the old Stadium and Shea, where the Mets and Yankees played a real Subway Series in 2000.

Four games this time. Two at Citi. Two at the Stadium next month. The Mets try to stop this freefall they’ve been in since getting swept by the Blue Jays at home the weekend before last, a stretch that has seen them lose eight out of nine and end up in a race to the bottom with the Nationals instead of a race to the top of the NL East with the Braves.

The Yankees? They just lost two of three to the last-place Red Sox at home, scoring a grand total of seven runs in the process, as they try not to fall further than the nine in the loss column they already are behind the Rays. You want to know why these first two Mets-Yankees games feel big this week?

Because both teams need them.

“But there’s always something more at play here,” Mets skipper Buck Showalter said. “Things that matter to our fans as much always should matter to us.”

Buck stopped managing the Yankees after the 1995 season. He didn’t manage his first Subway Series, as a Met, until last season. It means he missed a lot over the quarter-century, during which the Mets and Yankees started playing games for real. Trust me on something: It wasn’t just Mlicki surprising us by pitching the game of his life in June 1997.

There was the afternoon at Shea in 2002, two years after Roger Clemens had thrown that piece of broken bat at his nemesis Mike Piazza in the World Series that Shawn Estes, pitching for the Mets that year, threw behind Clemens when he came to the plate, hit a two-run homer off him later and pitched seven shutout innings himself.

David Wright walked off the great Mariano Rivera one time in 2006. So did Matt Franco with a single off Rivera two years into the rivalry, in ’99. Just two years ago, on the 20th anniversary of Sept. 11, Aaron Judge hit a memorable home run, a two-run shot that tied the game, before the Yankees won it.

There was the night in 2009, when the Mets were about to beat the Yankees in the bottom of the ninth at Yankee Stadium. Second baseman Luis Castillo was in short right field, camped underneath a popup that looked as if it would end it. But then the earth started spinning for poor Castillo, and the ball hit off his glove and fell to the ground and the Yankees were the ones who surprised us that night.

There was the Subway Series game in 2021, when Francisco Lindor hit three home runs for the Mets. A year before, the Yankees, in a seven-inning doubleheader game, scored five in their last ups to come back and win that one. Mets fans are still waiting for the grand slam that Piazza hit off Clemens in the summer of 2000 to come down. There was even the time, because of rainout scheduling, when the Mets and Yankees played games at Shea and the old Stadium on the same day.

Bobby Valentine, who managed the Mets for the first interborough game back in ‘97, once said this:

“We wanted to treat it like another ballgame. But we all knew it wasn’t.”

Still isn’t. Mets fans at Yankee Stadium trying to be louder than Yankee fans. Yankees fans at Citi Field trying to do the same. You have to be there.