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1.
Complimenting a person merely to gain something in return.
Joe: That automobile salesman sure thought you were a good driver. Did you hear all the compliments he gave you?

Bob: Yeah. He was just blowing smoke up my ass to get me to buy the car.
de Old Polecat 15 avril 2011
 
2.
Giving a gratuitous and insincere compliment, possibly to deceive. (Can be my, your, his, or her ass, but probably not plural, as in their asses.)
Yeah, sure. Thanks for the kind words, but I think you're blowing smoke up my ass.
de RSD 6 juillet 2006
 
3.
to bullshit or lie, to tell a falsehood. originally comes from the era of snake-oil salesmen and traveling hucksters pandering cure-all ointments.

one said cure for many ailments (including constipation) was a "tobacco enema" in which the purveyor would literally blow smoke up the afflicted's rectum with a device created solely for this purpose. obviously people caught on soon enough, and figured out that tobacco enemas were embarrassing as well as useless.

as such, the phrase became the euphemism it is today for selling a line of nonsense to an otherwise naive or unsuspecting rube.
person 1: "did you know that recent studies show that rat feces are as effective as any available wrinkle cream on the market?"

person 2: "you're totally blowing smoke up my ass"
de waterbrother 11 septembre 2009
 
4.
Most literally translating to "trying to get a reaction" out of somebody. Originated from a 16th century technique to determine death by literally blowing tobacco smoke into someone's anus (through a long pipe) - where a reaction indicated that the person was still alive.
Guy 1: Hey man, I think someone just stole your car!
Guy 2: Are you blowing smoke up my ass?
de Med Student 30 novembre 2005