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This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the "$\lambda$-topology". This classification theorem allows us to generalize some geometric results from the paper ("Lambda-Topology vs.doi:10.1088/0951-7715/21/10/004 fatcat:t7smmjbkrnfvda6ugvdmvvqbfa