Many practical applications of high Tc superconductors involve layered materials and magnetic fields applied on an arbitrary direction with respect to the layers. When the anisotropy is very large, Cooper pair currents can circulate either within or perpendicular to the layers. Thus, tilted magnetic fields lead to intertwined lattices of Josephson and Abrikosov vortices, with quantized circulation across and within layers, respectively. Transport in such intertwined lattices has been studied in detail, but direct observation and manipulation of vortices remains challenging. Here we present magnetic force microscopy experiments in tilted magnetic fields in the extremely quasi-two dimensional superconductor Bi2Sr2CaCu2O8. We trigger Abrikosov vortex motion in between Josephson vortices, and find that Josephson vortices in different layers can be brought on top of each other. Our measurements suggest that intertwined lattices in tilted magnetic fields can be intrinsically easy to manipulate thanks to the mutual interaction between Abrikosov and Josephson vortices.