Before revision:  A bistellar flip on a partial triangulation either flips an edge  , removes a non-extreme point of degree 3, or adds a point in P \setminus P' as vertex of degree 3.
After revision:  A bistellar flip on a partial triangulation either flips an edge , removes a non-extreme point of degree 3, or adds a point in P \ P' as vertex of degree 3.