\sim_0$[$S_{0}$]{}]{};  (removeOnePod00) at (0,-0.0)  \(0) at (-0.0,0) ; (0b) at (-0.0,-0) ; (0) at (-0.0,0) ; (0b) at (-0.0,0) ; (0c) at (-0.00,0) [$S$]{}; (-0,0) - (-0.00,0.0); (-0,0) - (-0.00,-0.0); (-0.00,0.0) arc (000:000:0.0); (0) - (0); (0) - (0b); (0) - (0b);  (-0.0,0) node [+]{};  (0,0) - (0.00,0.0); (0,0) - (0.00,-0.0); (0.00,0.0) arc (000:000:0.0); (0b) at (0.00,0) [$S$]{}; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,-0) ; (0b) at (0,-0) ; (0) at (0,0) ; (0) at (0,0) ; (0) - (0); (0) - (0); (0) to (0); (0) to (0); (0) - (0b);  ; (removeTwoPod00) at (0,-0)  \(0) at (-0.0,0) ; (0b) at (-0.0,-0) ; (0) at (-0.0,0) ; (0b) at (-0.0,0) ; (0c) at (-0.00,0) [$S$]{}; (-0,0) - (-0.00,0.0); (-0,0) - (-0.00,-0.0); (-0.00,0.0) arc (000:000:0.0); (0) - (0); (0) - (0b); (0) - (0b);  (-0.0,0) node [+]{};  (0,0) - (0.00,0.0); (0,0) - (0.00,-0.0); (0.00,0.0) arc (000:000:0.0); (0b) at (0.00,0) [$S$]{}; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,-0) ; (0b) at (0,-0) ; (0) at (0,0) ; (0) at (0,0) ; (0) - (0); (0) - (0); (0) to (0); (0) - (0);  ; (removePod00) at (00,-0.00)  \(0) at (-0.0,0) ; (0b) at (-0.0,-0) ; (0) at (-0.0,0) ; (0b) at (-0.0,0) ; (0c) at (-0.00,0) [$S$]{}; (-0,0) - (-0.00,0.0); (-0,0) - (-0.00,-0.0); (-0.00,0.0) arc (000:000:0.0); (0) - (0); (0) - (0b); (0) - (0b);  (-0.0,0) node [+]{};  (0,0) - (0.00,0.0); (0,0) - (0.00,-0.0); (0.00,0.0) arc (000:000:0.0); (0b) at (0.00,0) [$S$]{}; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,-0) ; (0b) at (0,-0) ; (0) at (0,0) ; (0) at (0,0) ; (0) - (0); (0) - (0); (0) to (0);  ; (00,-0.00) node [${\mathcal{P}}$]{};  (removeOnePod0) at (0,-0.0)  \(0) at (-0.0,0) ; (0b) at (-0.0,-0) ; (0) at (-0.0,0) ; (0b) at (-0.0,0) ; (0c) at (-0.00,0) [$S$]{}; (-0,0) - (-0.00,0.0); (-0,0) - (-0.00,-0.0); (-0.00,0.0) arc (000:000:0.0); (0) - (0); (0) - (0b);  (-0.0,0) node [+]{};  (0,0) - (0.00,0.0); (0,0) - (0.00,-0.0); (0.00,0.0) arc (000:000:0.0); (0b) at (0.00,0) [$S$]{}; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,-0) ; (0b) at (0,-0) ; (0) at (0,0) ; (0) at (0,0) ; (0) - (0); (0) - (0); (0) to (0); (0) to (0); (0) - (0); (0) - (0b);  ; (removeOnePod0B) at (00,-0.0)  \(0) at (-0.0,0) ; (0b) at (-0.0,-0) ; (0) at (-0.0,0) ; (0b) at (-0.0,0) ; (0c) at (-0.00,0) [$S$]{}; (-0,0) - (-0.00,0.0); (-0,0) - (-0.00,-0.0); (-0.00,0.0) arc (000:000:0.0); (0) - (0); (0) - (0b);  (-0.0,0) node [+]{};  (0,0) - (0.00,0.0); (0,0) - (0.00,-0.0); (0.00,0.0) arc (000:000:0.0); (0b) at (0.00,0) [$S$]{}; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,0) ; (0) at (0,-0) ; (0b) at (0,-0) ; (0) at (0,0) ; (0) at (0,0) ; (0) - (0); (0) to (0); (0) to (0); (0) - (0); (0) - (0b);  ; (00,-0.00) node [${\mathcal{P}}$ by]{}; (00,-0.00) node [**Case 0**]{};  (orig) - (0.0,0) \[-&gt;\] (0.0,0) |- (removeTwoPod0); (removeTwoPod0) - (removeTwoPod0B); (orig) - (0.0,0) \[-&gt;\] (0.0,0) |- (removeOnePod00); (orig) - (0.0,0) \[-&gt;\] (0.0,0) |- (removeTwoPod00); (removeOnePod00) - (removePod00); (removeTwoPod00) - (removePod00); (orig) - (0.0,0) \[-&gt;\] (0.0,0) |- (removeOnePod0); (removeOnePod0) - (removeOnePod0B);  **Case 0 :** [$S_{0,0}$]{} $\sim_0$ [$S_{0,0,0}$]{}  Figure \[fig:pod00EQUIV0pod000\] shows the possible moves on [$S_{0,0}$]{} or [$S_{0,0,0}$]{}, and the answer leading to a ${\mathcal{P}}$-position (for readability, we write $S$ instead of $\hat{S}$ in the figure).  (orig) at (0,0) [ ]{};  (removeTwo