We investigated with XMCD-PEEM magnetic imaging the magnetization reversal processes of Neel caps inside Bloch walls in self-assembled, micron-sized Fe(110) dots with flux-closure magnetic state. In most cases the magnetic-dependent processes are symmetric in field, as expected. However, some dots show pronounced asymmetric behaviors. Micromagnetic simulations suggest that the geometrical features (and their asymmetry) of the dots strongly affect the switching mechanism of the Neel caps.