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
9 months into Maya...and still learning...
0 experience with any other 3D programs