Frazzled Fliers : Transportation: LAX is wrapped in the frayed nerves of arriving and departing passengers on the nation’s busiest travel day. Labor trouble at American and United airlines adds a few wrinkles on eve of holiday.

She was plenty thankful, a frazzled Patricia Martinez admitted.

Not for the turkey dinner she was headed for today in Culver City. But because she had escaped those turkeys at the Sacramento airport.

“First they delayed our flight three times. Then they canceled it,” the 22-year-old student at UC Davis moaned. “We were supposed to leave at 7:30 Tuesday night, then 9:20, then 11. Finally at 2 this morning they sent us home. We went back to the Sacramento airport at 9.”

Martinez and her 4-year-old son, Dylan, were standing Wednesday afternoon at Ground Zero in the air war: Outside the busiest terminal of the West’s busiest airport on the country’s busiest travel day of the year.

Thousands of passengers were descending on Los Angeles International Airport. And all were determined to get where they were going by dinnertime today--despite a pair of airline labor disputes that threatened to toss a couple of drumsticks into the works.

American Airlines was struggling to resume full service after a five-day walkout by flight attendants that grounded most passenger jets. And United Airlines was staggering from a one-day work slowdown by machinists protesting rejection of an employee buyout proposal.

Scott Perlmutter was hoping to find a last-minute American Airlines seat that would take him to a Thanksgiving family reunion in Miami.

“My original flight was canceled two days ago. I’m going to plead to get on today if I have to,” the 30-year-old Beverly Hills resident said.

American Airlines worker Vivianne Cardoza was sympathetic. She gave Perlmutter a motherly hug. “Don’t worry. We’ll get you home for Thanksgiving,” the 30-year airline veteran from Torrance promised.

“Only three flights out of 65 that we have here today have been canceled,” Cardoza said. “Our customers are being very patient.”

Relieved, too. The next counter over, Sunny Mindel, 35, of New York, beamed when she and friend Tom Rapier, 39, of Santa Monica, got seats to Dallas and on to Lubbock, Tex., where Rapier’s family is gathering today. American is the only airline that flies there, Mindel said.

“We have Katie, our cocker spaniel, with us. And I wasn’t looking forward to renting a car and driving six hours with her to Lubbock,” Mindel said. “I was a wreck thinking about it.”

Added Rapier, a television technician: “I’m pro-labor and pro-flight attendants. I’m glad the strike’s over so we can fly American.”

Some travelers weren’t in a chance-taking mood, however. They had frantically ditched American and scrounged seats on other carriers.

“My parents switched my ticket from American to United last Friday,” said Karen Hug, 19, a UCLA student returning home to Barrington, Ill. “I’ve missed flights here before. I didn’t want to get stuck again at LAX.”

Tuesday’s brief United slowdown was a particular jolt to the refugees from American.

“I got very nervous when I heard there was a United strike,” said Kryste Dawson, 27, of West Hollywood, who was headed for a visit with her parents in Littleton, Colo. “I’ve been planning this trip for months.”

Stephanie O’Rear, 28, was worried that a slowdown might shoot down her trip with friend Mike Carpenter, 29, to a family reunion in Great Falls, Va. Just in case, the Marina del Rey couple had lined up alternate plans: “We’ll turn around and go skiing,” O’Rear vowed.

The pair’s flight departed on time, however.

In United’s arrival area, Patricia Martinez wanted to know why a flight from Sacramento had taken 16 hours. She also was looking for her luggage.

“First they said a blizzard in Denver had delayed the plane. Then they said the plane was there but they were hunting for pilots to fly it. Then they said the plane had been snowed in in Chicago,” she said.

As for her suitcases: “They say my bags are at USAir.”