Mantle convection is a fundamental process in the Earth's system, yet its history remains poorly known. Sophisticated inverse geodynamic Earth models are available to retrodict past mantle states, but their high computational cost and complex parameterizations limit their ability to isolate key effects and interpret simulated paleo-mantle-flow patterns. This calls for an approach to conceptualize paleo-mantle-flow at a simple analytical level. The existence of weak asthenosphere allows one to formulate a Couette/Poiseuille model of upper mantle flow, where flow is linked to movements of overlying tectonic plates, and to lateral pressure gradients induced by rising plumes and sinking slabs. Here we present results from such models for the Atlantic realm in the Cenozoic, and link them to seismically inferred anisotropy along with mantle flow retrodictions from inverse geodynamic modeling. Our analytical paleo-mantle-flow indicates that (1) material sourced by plumes is carried towards slab locations, as expected, (2) it is broadly consistent with the orientation of seismic azimuthal anisotropy, and (3) it agrees with the large-scale flow patterns and amplitudes from mantle flow retrodictions. Our results suggest using a hierarchy of models together with growing geological constraints on past plate motions and dynamic topography to gain a better understanding of paleo-mantle-flow.