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Let (X, d) be a metric space and f1,infinity = {fn}infinity i=0 be a sequence of continuous maps fn : X -> X such that (fn) converges uniformly to a continuous map f. We investigate which conditions ensure that the transitivity of functions fn or the transitivity of the nonautonomous system (X, f1,infinity) is inherited to the limit function f and vice versa. Such problem has been studied for instance by A. Fedeli, A. Le Donne or J. Li who give different sufficient condition for inheriting of transitivity from fn to f. In this paper we give a survey of known result relating to this problem and prove new results concerning transitivity.