Visiting Montreal this week, and my Canadian accent ("aboot") has finally been explained to me as "Canadian raising" (contrast with "Canadian raisin"):
Apparently the difference is most easily demonstrated with the pronunciation of "loud" vs "lout". Unfortunately I don't have any Americans around right now to demonstrate to me how they do it differently. This calls for some experimentation when I get back to NYC.
Another one is "writer" vs. "rider." Apparently the 't' in the first word is pronounced like the 'd' in the second, but you can still tell them apart (in Canada) because the 'i' is pronounced differently. At least by Canadians. And possibly others because as Wikipedia claims, "it appears to be spreading."
None of this explains why Americans pronounce it "mawn treal" however.