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We continue our study of the Fourier-Stieltjes algebra associated to a twisted (unital, discrete) C * -dynamical system and discuss how the various notions of equivalence of such systems are reflected at the algebra level. As an application, we show that the amenability of a system, as defined in our previous work, is preserved under Morita equivalence. 2020 Mathematics Subject Classification: Primary 46L55; Secondary 37A55, 43A35, 46H25.doi:10.4064/sm190826-25-3 fatcat:xfqn4iipurbi3pev4b72ldufy4