 ${\Delta}'_b$ is a desired disk diagram ${\Delta}_{c}$ for $c$.  (-00,-0) arc (0:000:0); (-00,-0) node (v0) - (-00,-0); (-00,-0) -(-00,-0); (-00,0) -(-00.00,0); (-00,-0) \[fill = black\] circle (.00); (-00,-0) \[fill = black\] circle (.00); at (-00,-0) [$\Delta_{b_0}$]{}; at (-00,0.0) [$s_0$]{}; at (-00,