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“The storm has such a wide swath and so many major airports are involved that it’s going to take some time (to recover) because those airplanes are so far away,” said Ms. Gittens, who served as aviation director at Miami International Airport during several hurricanes from 2001 to 2004.

Airports in metropolitan New York were open, but air carriers were not operating. The Port Authority of New York and New Jersey said Monday that travelers shouldn’t even try to go to Kennedy, Newark Liberty, LaGuardia and Stewart airports.

JetBlue Airways Corp. canceled 1,200 flights for Sunday through Tuesday. The airline is hoping to resume flights at its Kennedy Airport hub Wednesday but is worried about flooding of the airport’s runways since they are all basically at sea level and near bodies of water, according to Rob Maruster, the company’s chief operating officer.

Delta has canceled 2,100 flights over the three days. American Airlines has scrapped 1,000 flights, including 260 on regional affiliate American Eagle.

The impact on airline’s bottom lines is unclear. Many of the customers on flights currently being canceled will reschedule later on, so the airlines will still collect the fares. But the cost of parking planes for days, along with potential damage, will undoubtedly cost airlines millions.

Travelers overseas could wait days to get to the East Coast of the U.S.

Frankfurt Airport in Germany canceled 12 incoming and nine outgoing flights because of the storm, adding to 12 it scrapped on Monday. Spain’s biggest airports in Madrid and Barcelona axed 19 flights, on top of 13 canceled the day before.

British Airways cut another 11 return flights to and from the East Coast on Tuesday, adding to 20 on Monday, when London’s Heathrow Airport canceled a total of 59 flights to and from the U.S.

Air India said its daily flights to Newark and JFK had been halted since Sunday.

South Korea’s Korean Air said it canceled three flights to New York and one flight to Washington on Monday and Tuesday. Asiana Airlines canceled its Tuesday flight to New York. Its Monday flight to JFK was delayed by 26 hours, then was postponed again by another 26 hours.

Hong Kong’s Cathay Pacific Airways had canceled six New York flights by Tuesday. The airline said another New York flight via Vancouver will only go as far as the Canadian city.

David Koenig in Dallas, Kate Brumback in Atlanta, Kelvin Chan in Hong Kong, Youkyung Lee in Seoul, Yuri Kageyama in Tokyo, David McHugh in Frankfurt and Ciaran Giles in Madrid contributed to this report.