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Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in $\\Bbb C^p$, for some $p>0$) or differentiable (parametrized by an open neighborhood of $0$ in $\\Bbb R^p$, for some $p>0$) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second family. Then, under which conditions are the two families locally isomorphic at 0? 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