The first train left the station at East 96th Street at noon after a speech by Democratic Gov. Andrew Cuomo, who pushed to meet a New Year’s Day deadline for the long-delayed project.

“I hope when you go down there you really feel how much hard work and time and patience it’s taken to get to this point,” Cuomo said. “It’s incredible. This is not your grandfather’s station.”

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The nearly 2-mile segment adds stations along Second Avenue at 96th, 86th and 72nd streets and a new connection to an existing subway line at 63rd Street.

Seen as crucial to alleviating congestion in the nation’s biggest subway system, it is on a line expected to carry about 200,000 riders a day. The entire system transports about 5.6 million riders on an average weekday.

The mood was festive on the first train, with many riders wearing hats that read Second Avenue Station, including Jessica Hauser and her boyfriend, Neil Smith, who both live on the Upper East Side.

“I can see my friends in Brooklyn much easier now,” Hauser said. “It’s really great to have another subway nearby. I think it’s going to release a lot of pressure from the 4, 5 and 6 trains. Especially in the morning when I have to sometimes wait for a second or third train, since they’re so packed.”

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The city’s transportation board first envisioned a Second Avenue subway in 1929, but the stock market crash and the Great Depression derailed the plan.

Ground was broken in 1972, but a fiscal crisis in the city slammed the brakes on the project again. The project finally got into high gear when major tunneling work began in 2007.

The $4.4 billion section opening was initially supposed to be completed in 2013. Delays stemmed partly from concerns about construction noise.

Next, the line is slated to expand north into East Harlem. No date has been set for starting that phase of construction.