Great question!

There's an interesting comment at http://math.stackexchange.com/questions/204405/for-an-n-gon-how-many-fundamental-polygons-are-there

"we ... disallow discontinuities, [i.e] two A edges to be adjacent with "wrong" directions." In the first 3 polygons of the top row, the head of A or B is attached to its own tail so these are ignored.

Another insight is that the orientation of the arrows is a guide for attachment and is invariant if direction is inverted for all identical edges, say flip all A edges.

So the last two polygons on the top row give the same glueing for a sphere, just flip the direction of the red lines to turn one polygon in to the other.
On the bottom row you have: Real Project Plane, Klein Bottle, Torus and Real Project Plane again (invert the red lines to equal the 1st RPP).

Great question!

There's an interesting comment at https://math.stackexchange.com/questions/204405/for-an-n-gon-how-many-fundamental-polygons-are-there

"we ... disallow discontinuities, [i.e] two A edges to be adjacent with "wrong" directions." In the first 3 polygons of the top row, the head of A or B is attached to its own tail so these are ignored.

Another insight is that the orientation of the arrows is a guide for attachment and is invariant if direction is inverted for all identical edges, say flip all A edges.

So the last two polygons on the top row give the same glueing for a sphere, just flip the direction of the red lines to turn one polygon in to the other.
On the bottom row you have: Real Project Plane, Klein Bottle, Torus and Real Project Plane again (invert the red lines to equal the 1st RPP).