“…Proposition 7.2 (Heath-Kobayashi [5,Proposition 3.7]) If a link L has the property that thin position differs from bridge position, then there exists an ambient isotopy f s , such that L = f 1 (L) is h-equivalent to L and L has a tangle decomposition by a finite number of non-trivial, non-nested, flat face up, bowl like 2-spheres, each of which is incompressible in the link complement. In this decomposition we have a tangle "on top" (above P) with all of the incompressible 2-spheres below it connected by vertical strands.…”