It is known that the group of homeomorphisms of a non-compact, connected, metrizable manifold acts transitively on certain spaces of measures defined, among other properties, by their behaviour at the manifold's set of ‘ends’. As a generalization of previous work of Fathi in the realm of compact manifolds, it is shown that the given action admits a continuous section when restricted to ‘biregular’ homeomorphisms and measures. This result exhibits the isotropy groups of measure-preserving homeomorphisms as deformation retracts of the corresponding acting groups.