NEW YORK (CBSNewYork) — Subway safety was part of a fiery debate between the two Republican candidates for mayor. Fernando Mateo and Curtis Sliwa squared off Wednesday evening.

Mateo and Sliwa not only fought like cats and dogs, they fought over cats and dogs after Sliwa said as the owner of 15 rescue cats he would also run as the nominee of a new animal welfare party, CBS2’s Marcia Kramer reported.

“When I’m mayor, New York City will have no-kill shelters. We are not killing our friends,” Sliwa said.

“I’m a communicator,” Mateo responded. “He communicates with his 13 cats and his 14 litter boxes. Curtis Sliwa is a Guardian Angel. He should be a train conductor.”

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They fought about the best way to patrol the subways. Mateo said to put more cops on the platforms. Sliwa said more cops on the trains. And then they fired off more accusations against each other.

“Curtis, you gotta stop lying. You accused the police department cops of having kidnapped you and you admitted it was a lie,” Mateo said.

“Some of the guys who frequented your club ended up shooting me in the back of a cab in 1992. Members of organized crime,” Sliwa said.

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They also squabbled over who is the “real” Republican.

“Today we’re going to take the mask off his face and show every Republican out there who the true Republican is here,” Mateo said.

“And by the way, I was a registered Republican in New York City before you were,” Sliwa said.

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Both said they would have handled the pandemic or a future health crisis differently.

“We will never do what both de Blasio and Cuomo did to us — crush the life out of our city with these executive orders,” Sliwa said.

“I would do what our president did, what Donald Trump did at the time — follow the science,” Mateo said.

READ MORECandidate Conversations: Curtis Sliwa

There was also agreement on issues that traditionally divide Democrats and Republicans — cops don’t have to live in the five boroughs, the test for the special high schools should be the only entrance criteria, and public school students should not be required to get a COVID-19 vaccine.

But there was also this about respecting the NYPD:

“We have a department that has done the right thing for decades,” Mateo said.

“What revisionism. When the NYPD closed your club, La Marina, in Washington Heights, you publicly said that all those cops responsible for that, they should have their heads cut off like snakes,” Sliwa said.

READ MORECandidate Conversations: Fernando Mateo

A moment of relative calm came when the candidates were asked what they would do when the city reopens.

A sporting event?

A concert perhaps?

Both picked theater. Sliwa wants to see “Hamilton” and Mateo wants to attend “Jersey Boys.”

Marcia Kramer