Inertia-induced changes in transport properties of an incompressible viscous time-periodic flow due to fluid inertia (non-zero Reynolds numbers Re) are studied in terms of the topological properties of volume-preserving maps. In the non-inertial Stokes limit (vanishing Re), the flow relates to a so-called one-action map. However, the corresponding invariant surfaces are topologically equivalent to spheres rather than the common case of tori. This has fundamental ramifications for the response to small departures from the non-inertial limit and leads to a new type of response scenario: resonance-induced merger of coherent structures. Thus several coexisting families of two-dimensional coherent structures are formed that make up two classes: fully-closed structures and leaky structures. Fully-closed structures restrict motion as in a one-action map; leaky structures have open boundaries that connect with a locally-chaotic region through which exchange of material with other leaky structures occurs. For large departures from the non-inertial limit the above structures vanish and the topology becomes determined by isolated periodic points and associated manifolds. This results in unrestricted chaotic motion.