  For any primitive proper substitution \sigma, we give explicit constructions
of countably many pairwise non-isomorphic substitution dynamical systems
{(X_{\zeta_n}, T_{\zeta_n})}_{n=1}^{\infty} such that they all are (strong)
orbit equivalent to (X_{\sigma}, T_{\sigma}). We show that the complexity of
the substitution dynamical systems {(X_{\zeta_n}, T_{\zeta_n})} is essentially
different that prevents them from being isomorphic. Given a primitive (not
necessarily proper) substitution \tau, we find a stationary simple properly
ordered Bratteli diagram with the least possible number of vertices such that
the corresponding Bratteli-Vershik system is orbit equivalent to (X_{\tau},
T_{\tau}).
