Suppose $M_1 = \langle Q_1,S,R,f_1,g_1\rangle$ and $M_2 = \langle Q_2,S,R,f_2,g_2\rangle$ are two strongly connected machines.
I need to show that $M_1 \equiv M_2$ iff there exist a state $p \in Q_1$ and a state $q \in Q_2$ such that $p \equiv q$.
Thanks