Gov. Cuomo will never be confused with Fiorello La Guardia. “When I make a mistake, it’s a beaut,” the legendary mayor of New York once confessed.

Unfortunately, Cuomo’s pride and political calculations don’t allow him to admit error even as he finally reverses one of the mostly deadly policy mistakes in New York history.

Nursing homes and rehabilitation centers have tallied more than 5,000 coronavirus deaths, yet the governor accepts zero responsibility despite his March 25th order forcing them to take infected patients from hospitals.

Now he says they no longer have to do that, announcing Sunday that “a hospital cannot discharge a person who is COVID positive to a nursing home.”

Indeed, the initial order denied nursing homes the right even to ask if patients being sent by hospitals had tested positive for the coronavirus.

Now hospitals must do discharge tests and only those who are negative can be referred to nursing homes.

Said one nursing home executive, “It feels at least a month too late.”

The move comes amid growing calls for an independent investigation of the nursing home catastrophe, where the death count dwarfs the total deaths in every other state except New Jersey.

Still, Cuomo claims the reversal is not a reversal, nor is it a recognition of the fatal impact of the initial order.

“Whatever we’re doing has worked, on the facts,” he insisted.

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He should try selling that view to Maria Porteus. She lost her father, Carlos Gallegos, to the coronavirus in a Long Island nursing home last month soon after the state forced it to accept infected patients. She watched the governor Sunday and was left steaming.

“I’m still angry and I’m still hurt,” she said. “It’s a slap in the face for him because he’s not taking responsibility for what happened to my father and so many others.”

Porteus said she’s part of a Facebook group that has nearly 250 members who lost loved ones in nursing homes, adding: “The stories are all almost the same. And Cuomo’s still acting like he’s not the one who did this order, like it’s somebody else or it’s the nursing homes’ fault.”

Arlene Mullin, who lost her father under similar circumstances, also was unhappy with Cuomo Sunday. She said in an e-mail:

“In light of how many mothers lost their lives, it was distasteful to use his press conference as a tribute to his mother. He could have called her privately to wish her well on Mother’s Day. It was insensitive to those people whose mothers died in nursing homes due to his cruel policy.”

Cuomo insists the nursing homes “could have resisted” taking COVID-positive patients if they had no ability to care for them. The order, he seemed to be saying, was only meant to ensure that such patients were not discriminated against.

That point, he conceded, “was never really communicated,” as if the March 25 order was not meant to be taken verbatim.

So the only failure is a failure to communicate, though he didn’t specify whose failure that was. Certainly not his.

There are two gaping holes in that argument. First, nursing homes never believed they had any right to deny infected patients, saying the order from the state Department of Health would have included that option if that were the intent. The order’s language did not offer any hint of flexibility.

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“No resident shall be denied re-admission or admission to the NH solely based on a confirmed or suspected diagnosis of COVID-19,” it reads. “NHs are prohibited from requiring a hospitalized resident who is determined medically stable to be tested for COVID-19 prior to ­admission or readmission.”

Worse, the order came without warning, took effect immediately and gave the homes no time to set up segregated beds and staff.

All nursing homes, good and bad, large and small, were treated as if they were fit for an influx of coronavirus patients.

The second problem with Cuomo’s claim is the case of the Cobble Hill Health Center, which lost at least 55 patients to the virus. The CEO, Donny Tuchman, showed reporters April emails where he asked state health officials for assistance, and was turned down. He also asked them if COVID-19 patients he had could be sent instead to the Javits Center or the Navy ship Comfort, both of which were far below capacity. He was rejected again.

It’s true there was one way Albany officials did help beleaguered nursing homes. The packages of equipment they sent included body bags.