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By Reem Nasr, CNBC

New York Gov. Andrew Cuomo introduced a plan to completely overhaul LaGuardia Airport that comes with a $4 billion price tag for the first part. He made the announcement Monday at a luncheon detailing new infrastructure plans for his state. Vice President Joe Biden was at the meeting.

Biden, who last year compared the airport to something found in the "third world," fully supports the plan which will break ground next year. Total construction will take about 18 months, Cuomo said.

"It is actually happening," said Cuomo. "LaGuardia Airport is un-New York."

He said that approvals that would normally take years were expedited by the vice president's office.

The construction will create 8,000 jobs, Cuomo said. The overhaul will completely change LaGuardia's current design. Instead of a series of ad hoc terminals, the new airport will consist of one unified terminal that will have connection to mass transportation, including to rail and ferry.

The new airport will be moved about 600 feet closer to the Grand Central Parkway to create more space for flight operation, the governor said.

Gov. Andrew Cuomo introduced a plan Monday to redesign and rebuild LaGuardia airport, replacing the cramped, outdated hub with a unified facility.Reimagining New York

Biden praised Cuomo's efforts to push the plan forward. "This is the greatest city in the world and it requires 21st century infrastructure," the vice president said.

The plan to build a new airport could not be done without the full cooperation of Delta Air Lines since the carrier privately leases its own disparate terminals on the site. Cuomo called the company "a great corporate citizen."

Power outage at LaGuardia Airport causes 3-hour delays

John F. Kennedy International Airport will also receive improvements as part of the wider infrastructure overhaul. The airport will get its own new hotel, set to create about 3,700 jobs, Cuomo said.

Biden in February of last year said if he blindfolded someone and took him to LaGuardia, he'd think he was in "some Third World country." In October, Biden and Cuomo talked about plans to improve the region's airports and announced a design competition.

Meanwhile, earlier in the day at a news conference in Western New York, Biden and Cuomo revealed details about a photonics hub to be located in Rochester.

—The Associated Press contributed to this report.