Mitchell Moss, who was an adviser to former Mayor Michael R. Bloomberg, described the Cuomo-de Blasio relationship as one of “managed conflict.” All New York governors and New York City mayors are “natural enemies,” he said, often more so when they are members of the same political party.

“The mayor and the governor have different constituencies and different agendas,” said Mr. Moss, now the director of the Rudin Center for Transportation at New York University. “I think we’re going to see hand-to-hand combat, but fought in a kind of polite style.”

Yet the combat has not always been polite.

Before the mayor was sworn into office, Mr. Cuomo announced his opposition to upper-income tax increases Mr. de Blasio had campaigned on. In March, when Mr. de Blasio moved to block the expansion of charter schools in the city, Mr. Cuomo headlined a pro-charter rally in Albany.

Lately, Mr. Cuomo, always limited in his accommodation of Mr. de Blasio, has seemingly grown less patient. His decision to close the subways ahead of a late-January snowstorm, without advance notice to the mayor’s office, left heads spinning at City Hall. (In the midst of a conference call before the storm, one senior mayoral aide learned of the shutdown from an email alert, and said so to an official with the transportation authority, who had just stated on the call that mass transit would remain open. The official briefly exited the call before returning to confirm the shutdown.)

It was not Mr. Cuomo’s first instance of going it alone in an emergency: Last fall, he surprised Mr. de Blasio in the midst of the Ebola panic by announcing a strict quarantine policy for at-risk travelers.

Most startling to City Hall were Mr. Cuomo’s expressions of respect for Patrick J. Lynch, the police union leader who set off a political crisis for the mayor after two officers were murdered in December by saying that there was “blood on the hands” of the administration. Mr. Lynch, the governor said then, “represents the feelings of the police officers.”

Aides argued the relationship has produced results, whatever the rough patches.

“We look forward to continuing this partnership for years to come,” the governor’s chief spokeswoman, Melissa DeRosa, said.