This isn't exactly what you are looking for, but I believe you can algorithmically go between the AR-quivers of orientations related by source/sink mutations (also called APR mutations). This corresponds to flipping the direction of all arrows incident to a source or a sink.

Right. By ``similar formula of arbitrary degree'' I'm asking for the integral over a cycle of the appropriate dimension.

The link appears to be broken. Do you know the title of the work it is supposed to link to?

@Chris: try section 4.2 of "Koszul duality for Operads" by Ginzburg and Kapranov (arxiv.org/abs/0709.1228). The arXiv version doesn't seem to have any pictures though...

True, it's not simply connected but that's not so important for what I want (elliptic curves aren't simply connected but are still CY enough for MS)

Ahh.. the final nail in the coffin. Thanks