Is the flip of the cis-isomer wrong? Specifically the image on the bottom right.
What I see is that on the cis-isomer in the first chair, we have an axial upward methyl group and an equatorial upward methyl group. When the ring flips we now have an equatorial upward methyl group (good) and a downward equatorial methyl group (bad). Shouldn't the second one be axial upward? From what I understand, ring flips shouldn't change the orientations of groups; just their axial/equatorial configurations.
Also, in general, would these two rings be equivalent?