Three-dimensional advection of passive tracers in non-inertial flows is studied in a finite cylinder confined by two parallel endwalls by means of numerical simulations and laboratory experiments. The fluid is set in motion through steady or time-periodic forcing by in-plane motion of the endwalls via a given forcing protocol. The numerical analysis centres on a dynamical-systems approach and concerns symmetry-based identification of coherent structures in the web of tracer paths (collectively defining the flow topology) for a number of archetypal flow configurations. The role of the flow topology in the process of tracer transport is investigated by numerical tracking of finite-size material objects released at strategic locations in the flow. Experimental validation of key aspects of the numerical results has been carried out in laboratory experiments by flow visualization with dye and flow measurement via three-dimensional particle tracking velocimetry.