(L-R) New York City Republican mayoral candidates Joe Lhota, George...

(L-R) New York City Republican mayoral candidates Joe Lhota, George McDonald, and John Catsimatidis participate in a primary mayoral debate at the WABC/Channel 7 studios in Manhattan (Aug. 9, 2013) Credit: James Keivom

The Republicans hoping to succeed Michael Bloomberg debated head-to-head for the first time Friday, jousting over who would be the best successor.

"Mike Bloomberg's 12 years in office have been very, very good," said Joe Lhota, a former MTA chief.

"Some of our Democratic opponents are about tearing down what Mike Bloomberg has done. I believe that New York City has never been in better shape," said George McDonald, an advocate for the homeless.

From the NYPD's controversial stop-and-frisk tactic to how Bloomberg has steered city schools, the men said during a debate at the WABC/7 studios that they'd build on what Bloomberg, a Republican turned independent, and predecessor Rudy Giuliani, a Republican, accomplished.

John Catsimatidis, owner of the Gristedes grocery stores, also said he would try to lure the best teachers by offering them help with apartments, and that he would freeze taxes.

Lhota said he would make sure garbage gets picked up and snow removed. He said he would put the city "through a budget diet," and that he would not award back pay to unions and wouldn't raise taxes.

McDonald said he would work to guarantee employment for everyone. On taxes, he said only he doesn't want to raise them.

In general, the candidates disagreed with Bloomberg only on minor points: Lhota, over Bloomberg's soda ban, and Catsimatidis, over Bloomberg's bike lanes that crisscross the city, saying they prevent fire trucks from reaching their destinations.

Lhota, who worked as Giuliani's budget chief, said his former boss was the right steward at the right time for a crime-ridden city. But he said he would be his own man.

"Rudy Giuliani and Joe Lhota are two very, very different people," Lhota said. He added: "Next January will be the first term of Lhota, not the third term of Rudy Giuliani."

McDonald argued that racial tension rose during Giuliani's mayoralty.

A Marist poll in June put Lhota at the top of the GOP race, with 28 percent of registered Republicans, Catsimatidis with 21 percent and McDonald with 10 percent.

The candidates have been struggling to get publicity for their campaigns, with much attention focused on Democratic rival Anthony Weiner and the scandal surrounding his cyber-sexting. All three Republicans said Weiner should get out of the race. "The press has focused on Anthony, Anthony, Anthony, and that's a big mistake," said Lhota.

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