The blood flow through our microvascular system is a renowned difficult process to understand because the complex flow behavior of blood is intertwined with the complex geometry it has to flow through. Conventional 2D microfluidics has provided important insights, but progress is hampered by the limitation of 2-D confinement. Here we use selective laser-induced etching to excavate non-planar 3-D microfluidic channels in glass that consist of two generations of bifurcations, heading towards more physiological geometries. We identify a cross-talk between the first and second bifurcation only when both bifurcations are in the same plane, as observed in 2D microfluidics. Contrarily, the flow in the branch where the second bifurcation is perpendicular to the first is hardly affected by the initial distortion. This difference in flow behavior is only observed when red blood cells are aggregated, due to the presence of dextran, and disappears by increasing the distance between both generations of bifurcations. Thus, 3-D structures scramble in-plane flow distortions, exemplifying the importance of experimenting with truly 3D microfluidic designs in order to understand complex physiological flow behavior.