Amid their ever-deepening rift, Mayor de Blasio will head upstate Wednesday for Gov. Andrew M. Cuomo’s State of the State speech, kicking off his annual rite of lobbying Albany for funding and policies that benefit the city.

De Blasio also will be contending with a changed leadership landscape as he presents a now-familiar agenda, including mayoral control of schools, funding for universal pre-K and the continuation of the real-estate tax abatement program, 421-a.

As of Sunday, City Hall still had not yet been briefed on the contents of Cuomo’s annual address, de Blasio spokeswoman Karen Hinton said. The governor, however, has signaled that he will announce new policies that affect homeless shelters — a focus of recent sniping between the mayor and governor.

The legislative session will be the first since the mayor in June accused Cuomo, a fellow Democrat, of conducting a “vendetta” against those who would oppose him. De Blasio has stood by his comments, saying last Wednesday that he will be “straightforward” in calling out the governor and the state if they act against city interests.

Mayoral aides have been meeting with state lawmakers “to push not only the city’s agenda but also ensure legislators’ concerns and policy needs are heard,” Hinton said in a statement. “It’s a two-way street, and we want to build a partnership with them to serve all New Yorkers.”

Even Democrats last year complained de Blasio’s team didn’t do enough listening. “Nobody likes to be dictated to,” Assemb. Phil Goldfeder (D-Queens) told Newsday last summer.

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Political experts said Cuomo, if he chooses, can present a hurdle to de Blasio’s needs.

“The session will be more or less difficult — I think, in many ways — depending on the actions of the governor,” said Baruch College political scientist Douglas Muzzio.

Cuomo has not said whether he will help with any items on de Blasio’s wish list. A spokeswoman for the governor, Dani Lever, declined to comment.

De Blasio will ask for renewed control of public schools for longer than a year and will mobilize business, religious and civic leaders to speak up on his behalf, City Hall officials said. He may appeal to past mayors, including Michael Bloomberg, to join the cause, officials said.

Last year, de Blasio lowered his target to three years from permanent renewal. The session ended with just a one-year extension, and Cuomo said the mayor may come back to ask for more “if he does a good job.”

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Joining Cuomo this year as the “three men in a room” are Senate Majority Leader John Flanagan (R-Northport) and Assembly Speaker Carl Heastie (D-Bronx), taking up the posts after Dean Skelos and Sheldon Silver were convicted separately on corruption charges.

Heastie supports a seven-year extension of mayoral control, his spokesman Michael Whyland said. Flanagan spokesman Scott Reif did not respond with comment to a question on the city’s agenda.

De Blasio will also request funding for supportive housing that combines residences with social services for homeless New Yorkers, City Hall officials said.

“We obviously want to see progress on supportive housing,” de Blasio said last Monday, adding the city has done its part. “We need help from the state as well.”