A Banach space is called (almost) transitive if the isometry group acts (almost) transitively on the unit sphere. The main problems around transitivity are the Banach-Mazur conjecture that the only separable and transitive Banach spaces are the Hilbert ones (1930) and the Wood conjecture that C_0(L) cannot be almost transitive in its natural supremum norm unless L is a singleton (1982). In this note we give necessary and sufficient conditions on the locally compact space L for the (almost) transitivity of C_0(L). This will clarify the topological content of Wood's problem.