I just got my first ever square one ( a Rubik's cube related puzzle ) and I have this case which I can't find any help on. An adjacent edge swap, with the equator solved. There is the parity algorithm which switches the two adjacent pieces BUT it also flips the equator. Help?
If you reach the last step after all parities are solved, and your middle layer is flipped, you can flip it with
/ (6, 0) / (6, 0) / (6, 0). If you're not sure what this looks like, or want a video, see this one. Other than that, though, you've got the right algorithm. You can do the parity algorithm you know.
Perform your parity algorithm to swap those two edges, then flip the equator back, and you're solved.