U.S. airline shares rallied on Wednesday, partially erasing two days of steep losses, as markets decided that the swine flu outbreak might not significantly crimp travel demand.

UAL Corp , parent of United Airlines, gained 3.22 percent to $5.21 on Nasdaq in early afternoon trading. Delta Air Lines gained 3.95 percent to $6.32 on the New York Stock Exchange. The Amex airline index <.XAL> was up 3.6 percent.

I don't currently see (swine flu) as a huge risk to airlines, said Jim Corridore, an analyst at Standard & Poor's Equity Research. I expect it to be largely localized to Mexico, which is a very small revenue generator for the U.S. airline industry.

The huge drop that we had over the last few days has gone too far in terms of discounting the risks of it, Corridore said.

Airlines shares fell sharply on Monday and Tuesday on expectations the flu would drain travel demand or prompt governments to restrict international flights.

The disease, which has killed 159 people in Mexico, has shown up in other countries, including the United States. On Wednesday, U.S. health officials confirmed that a baby in Texas died from the virus. It was the first confirmed death related to swine flu outside of Mexico.

LITTLE IMPACT

Some governments have warned travelers to avoid Mexico. But U.S. airlines said they have seen little impact. No major carrier has reported canceling flights because of the flu.

US Airways Group , which flies to 11 cities in Mexico, said the airlines' reservation centers received a surge in calls from concerned travelers on Monday, but call volume has declined.

We're obviously monitoring demand and we'll adapt accordingly, said US Airways spokesman Jim Olson.

Olson said some passengers are taking advantage of temporary ticket change fee waivers to move their leisure trips from Mexico to the Caribbean.

AMR Corp , parent of American Airlines, also has temporarily waived its ticket change fees on trips to Mexico. But the airline, which serves 14 Mexican cities, said that its operations have so far been unaffected.

There has been no indication from the Obama administration that a Mexico travel ban is warranted. But U.S. airlines are free to cancel flights on their own.

The U.S. government has not ordered any measures to actively screen airline passengers arriving and departing from Mexico.

This situation does not lend itself to that type of control measure, said Katherine Andrus, assistant general counsel for the Air Transport Association, the chief lobbying group for airlines.

There has been no discernible change in bookings to Mexico, Andrus said.

(Additional reporting by John Crawley in Washington; Editing by Brian Moss)

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