NEW YORK — It’s been an on-again, off-again, “believe it when you see it” project since the Jazz Age. Construction started 45 years ago.

But New Yorkers’ long wait to take a subway under Manhattan’s far Upper East Side ends Sunday, when a stretch of the new Second Avenue line opened to the public.

A ceremonial first ride took place on Saturday night for an invitation-only crowd of dignitaries, about 90 minutes before the New Year’s Eve ball drop in Times Square.

Everyday New Yorkers get their first chance to ride at noon on New Year’s Day, an opening date Democratic Gov. Andrew Cuomo made a priority in recent weeks. At the ceremonial ride Saturday, he described the importance of meeting the New Year’s deadline as a matter of pride.

“We needed to get this done on deadline because we’re New York and when we set the deadline, we’re going to get it done,” he said. “We needed to show people that government works, and we can still do big things and great things and we can still get them done.”

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 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 Sunday 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.