Planar flow past multiple successive blades and wakes is studied for nearly aligned configurations with normal non-symmetry inducing lift. The typical blade lies relatively near the centreline of the oncoming wake from the preceding blade. The central motion over a wide parameter range is in condensed periodic boundary layers and wakes with fixed displacement, buried within surrounding incident shear flow. This is accompanied, however, by streamwise jumps in the pressure, velocity and mass flux, across the leading edge of each blade, a new and surprising feature which is supported by the combination of incident shears and a solid surface and which is related to the normal flow through the multi-blade system. The leading-edge jumps are required in order to satisfy the equi-pressure condition at the trailing edge. Computational results include separating flows and show the lift and drag, and these are followed by a short-blade analysis which captures the main flow properties explicitly. The results agree qualitatively with experiments and direct simulations for rotor blade flows. The jump feature also extends for example to a single blade immersed in the relatively large wake of an upstream blade.