"There is a left side swing in the feather step and a right side swing in the three step. My question: Does the left side swing continue into the first step of the reverse turn or is it nutralized?"
The problem with your question is that you are confusing swing and sway.
Swing is an action, a type of movement.
Sway is a position.
You can't neutralize from an action, you can only take an action to neutralize from a position.
As for the right sway in the feather, much of that will have dissolved by then end of the third step of the feather. The left swing is really focused on step one to step two of the feather, and as a result the right sway is most apparent during step two to early step three.
Generally, upswings involve sway wheras downswings tend to be more vertical, in part because sway on a downswing would tend to result in crushing the backwards partner into the floor. It's okay for someone to be on top when the distance between the person underneath and the floor is increasing - but it's a bit more problematic for the person underneath when the distance between the person on top and the floor is decreasing!
