  We compute and analyze couples of ground states of 3D spin glass systems with
the same quenched noise but periodic and anti-periodic boundary conditions for
different lattice sizes. We discuss the possible different behaviors of the
system, we analyze the average link overlap, the probability distribution of
window overlaps (among ground states computed with different boundary
conditions) and the spatial overlap and link overlap correlation functions. We
establish that the picture based on Replica Symmetry Breaking correctly
describes the behavior of 3D Spin Glasses.
