  We study the transport of classical waves through three-dimensional (3D)
anisotropic media close to the Anderson localization transition. Time-,
frequency-, and position-resolved ultrasonic measurements are performed on
anisotropic slab-shaped mesoglass samples to probe the dynamics and the
anisotropy of the multiple scattering halo, and hence to investigate the
influence of disorder on the nature of wave transport and its anisotropy. These
experiments allow us to address conflicting theoretical predictions that have
been made about whether or not the transport anisotropy is affected by the
interference effects that lead to Anderson localization. We find that the
transport anisotropy is significantly reduced as the mobility edge is
approached---a behavior similar to the one predicted recently for matter waves
in infinite anisotropic 3D media.
