  We study b-arc foliation change and exchange move of open book foliations
which generalize the corresponding operations in braid foliation theory. We
also define a bypass move as an analogue of Honda's bypass attachment
operation.
  As applications, we study how open book foliations change under a
stabilization of the open book. We also generalize Birman-Menasco's
split/composite braid theorem: Closed braid representatives of a split (resp.
composite) link in a certain open book can be converted to a split (resp.
composite) closed braid by applying exchange moves finitely many times.
