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We study the role that Hamiltonian and symplectic diffeomorphisms play in thedeformation problem of coisotropic submanifolds. We prove that the action byHamiltonian diffeomorphisms corresponds to the gauge-action of the$L_\infty$-algebra of Oh and Park. Moreover we introduce the notion of extendedgauge-equivalence and show that in the case of Oh and Park's $L_\infty$-algebraone recovers the action of symplectic isotopies on coisotropic submanifolds.Finally, we consider the transversally integrable case in detail.

Equivalences of coisotropic submanifolds