  We report an in-depth investigation of the Anderson localization transition
for classical waves in three dimensions (3D). Experimentally, we observe clear
signatures of Anderson localization by measuring the transverse confinement of
transmitted ultrasound through slab-shaped mesoglass samples. We compare our
experimental data with predictions of the self-consistent theory of Anderson
localization for an open medium with the same geometry as our samples. This
model describes the transverse confinement of classical waves as a function of
the localization (correlation) length, $\xi$ ($\zeta$), and is fitted to our
experimental data to quantify the transverse spreading/confinement of
ultrasound all of the way through the transition between diffusion and
localization. Hence we are able to precisely identify the location of the
mobility edges at which the Anderson transitions occur.
