I'm still pretty new to maya, but here's what i would do.

I would merge two or more vertexes together.
to do that, combine the two polygons--shift select two polygon > combine

then go into vertex mode > select two or more vertex > snap vertexes together that you want to be togehter using the move tool and with (snap onto ponts) checked on.

Then > edit polygon > merge vertex

Do that to all the vertex that will be combining the two poly edges together

Not sure if that's any help, but yeah, just thought i give it a shot