Check out this video that I made to help your understand transverse flow effect. So many people get this confused during their private pilot helicopter training. I explain it a bit different than some and hope this helps. Everyone learns differently.
In order to understand transverse flow effect, you must first understand gyroscopic recession and how relative wind changes the angle of attack on take off.
When in doubt, always go to the Helicopter Flying Handbook for "the answer".
Transverse Flow Effect in a helicopter