are linen strops reversible?

i notice on my hanging strop, the leather and linen are secured with a twist-screw

i presume this means i may reverse (turn over) the linen strop at will? are the reverse sides also treated in the same way?

I just unscrewed mine yesterday, washed the linen in the bathtub, then reversed it and screwed it back together. It's a vintage strop and someone seemed to have put an abrasive on the linen.

I used it this morning and the results were great, no problems.

I can't imagine why reversing the linen would ever be a problem.