The propagation of extragalactic cosmic rays in the Galactic magnetic field plays a crucial role in understanding the cosmic ray signal measured at Earth. This is particularly true for the energy range where the transition from Galactic to extragalactic cosmic rays occurs $(E \approx 10^{15.5-18.5} \, {\rm eV})$. The reason for this is that the Galactic magnetic field strength is such that cosmic ray propagation in this energy range will change from diffusive to ballistic and is thus central to understanding the exact nature of the source transition.

Using simulation studies with CRPropa3, we study the effects that propagation in the Galactic magnetic field will imprint on cosmic rays in the rigidity range $10^{16-20} \, {\rm V}$ for both isotropically and anisotropically injected extragalactic cosmic rays. As a result, in case of isotropic injection we find that the Galactic magnetic field neither modifies the flux nor the arrival direction distribution across the entire rigidity range. For injection of dipole-like flux anisotropies as well as for single point sources, we find flux modifications across the entire rigidity range which depend on the direction and nature of the anisotropy. We also find that the arrival direction distribution is consistent with isotropy below rigidites of $10^{18} \, {\rm V}$, and the remaining anisotropy for all particles integrated above rigidities of $10^{18} \, {\rm V}$ manifests in the form of dipoles at the $1-10 \, \%$-level.