  We study the effects of the galactic magnetic field on the ultra high energy
cosmic ray propagation. We show that the deflections of the cosmic ray
trajectories can have many important implications such as (de)magnification of
the cosmic ray fluxes by lensing effects (which can modify the spectrum of
individual sources), the formation of multiple images of a source or the
existence of regions of the sky to which the Earth is almost blind. The
appearance of image pairs is related to the existence of critical curves in the
magnification maps, which divide regions in the sky where the images have
opposite parities. The results are pictorially illustrated as the stretching
and folding of a `sheet' describing the sky seen on Earth. Making use of the
most energetic AGASA events we emphasize the need to know the cosmic ray
composition and the structure of the magnetic field when attempting to do
detailed cosmic ray astronomy.
