New York yellow cab driver Douglas Gukdeniz, left, poses with Bob, right, and Betty Matas and one of their cats at their home in Queens.

AP / David Pollack

NEW YORK — A New York taxi driver agreed to take a couple and their two cats 2,500 miles into retirement in Arizona because, he figured, it would be something to remember.

“This job is not easy, and I want to do something different,” said Douglas Guldeniz, 45, who has been driving a taxi for two years. “I want to have some good memories.”

The three, plus cats, embarked on their four-day journey to Sedona, Ariz., on Tuesday night from the couple’s home in Queens’ Forest Hills neighborhood.

Like many New Yorkers, Betty and Bob Matas don’t drive, and they didn’t want their cats to travel in an airliner cargo hold.

Their solution: “Taxi!” — one of the most-used words in the city.

The septuagenarians met Guldeniz about three months ago, when they hailed his cab in Manhattan after a shopping trip.

They got to talking about their upcoming move, and, “We said, ‘Do you want to come?’ ” said Bob Matas, 72, a former audio and video engineer for advertising agencies. “And he said, ‘Sure.’ ”

They were kidding at first, Matas said, but as they talked over the ensuing weeks the gag became reality. Betty Matas, especially, is adventurous, and they both like the idea of a road trip, taking pictures along the way.

Their journey began on Tuesday evening after a final flurry of packing delayed them a few hours. They finally left at about 8:58 p.m., Guldeniz said by cell phone. The group had gone 65 miles, he said, crossing from Manhattan to New Jersey, before stopping before midnight for a bite to eat at a diner in Clinton.

Guldeniz will drive his canary-colored Ford SUV cab about 10 hours a day for $3,000 plus gas, meals and lodging. Since the SUV is a hybrid-electric vehicle, gas should cost about $300 one way.

As for the fare — it’s a deal. The standard, metered fare would be about $5,000 each way, said David Pollack, executive director of the Committee for Taxi Safety, a drivers’ group. But city Taxi and Limousine Commission rules direct drivers and passengers to negotiate a flat fare for trips outside the city and some suburbs.

The cats, Cleopatra and Pretty Face, will ride in the back in their travel cases. The taxi will follow the U-Haul truck transporting the family’s belongings.

“It’s a great way to see the country, see all the people, quickly,” said Betty Matas, 71, a retired executive administrative assistant.

She added: “It’s fun. We’ll take pictures, relax, read, eat.”

When they hit mountainous areas where cell phones don’t work, they have walkie-talkies to communicate with the friend driving the truck.

The couple trust their driver, whom Bob Matas described as “a very honest, sincere man.” Guldeniz, a native of the Turkish port city of Iskenderun, came to the United States in 1995.

“When people take my car, everybody is happy. They say it’s clean, and good for pictures — you see well because it’s higher than other cars and brighter inside,” said the cabbie, who lives in Brooklyn with his wife, 17-year-old son and 15-year-old twins, a boy and a girl.

They plan to take Route 81 all the way to Little Rock, Ark., “and if the weather is good, we take Route 40,” he said. “If the weather is bad, we’ll take Route 10.”

It should be a looooong conversation. Guldeniz is the real thing: a chatty New York cabbie.