This week, the mayor and the police commissioner were at odds—this time over the interpretation of a controversial report on black poverty in America. This is not the first time the two have split publicly, disagreements that officials are quick to downplay. We take a look at the relationship between the mayor and his police commissioner—a relationship that some describe as mutually beneficial. NY1's Courtney Gross filed this report.

It's been 21 months since Mayor Bill de Blasio named Bill Bratton his top cop.

"He and I don't necessarily agree on everything," Bratton said on NY1 earlier this week.

We saw that again this week. 

"Prescient" was how Bratton described the controversial decades-old Moynihan report, which argues the disintegration of a family unit is the cause of black poverty.

"Go read that again. Talk about being prescient about what was going to happen," Bratton said on MSNBC's "Morning Joe."

"I happen to disagree on this matter," the mayor said in response.

Go back a few months and look at the hiring of new police officers. Bratton wanted more. De Blasio did not. The mayor caved.

"He proved to me," de Blasio said.

Time and again, their relationship is tested. Each time, Bratton speaks up. 

"Police commissioner also needs to know that he works for the mayor. Certainly Bratton understands that, expecially after having dealt with Mayor Giuliani 20 years before," says police columnist Leonard Levitt, author of NYPD Confidential.

"I am leaving an organization that I have come to love dearly," Bratton said in 1996.

Bratton left the Giuliani administration after just two years—an early departure largely attributed to these two competing for the spotlight.

"We had our differences, but some of those differences were created by me," Bratton said recently.

"Whatever issues existed between Bill Bratton and Rudy Giuliani were fundamentally about personality. The issues that seem to exist between Bill Bratton and Bill de Blasio are fundamentally about policy," says former Deputy Mayor Randy Mastro.

One official here at City Hall described the relationship as a partnership, saying Bratton and de Blasio agree on the most fundamental principles and that includes community policing and broken windows.

Bratton has seemed to exert a certain independence similar to his predecessor Ray Kelly.

On a day-to-day basis, we're told Bratton does not seek approval from City Hall to make decisions—only when it's necessary. 

It's an independence Bratton may get because he is central to the mayor's success—a crucial ally as de Blasio bats away criticism of so-called disorder.

Bratton, at least publicly, returns the favor.

"There is nothing I haven't asked for that I haven't gotten so I guess that's pretty good expression of support," he said in June.