In this chapter we shall prove that there exists a finite set of simple, or elementary, moves (also called rules) on labelled apparent contours, such that the following property holds: two images of two stable embeddings of a closed smooth (not necessarily connected) surface are space isotopic if and only if their apparent contours can be connected using finitely many isotopies of the plane, and a finite sequence of elementary moves or of their inverses (sometimes called “reverses”).
