General anesthesia provides a reversible means of investigating the dynamical conditions required for consciousness. Within the Geometro-Diffusion Theory (GDT), loss of consciousness occurs when neural signal propagation no longer generates a sufficiently differentiated geometry whose relational information can be intrinsically accessed by the system. We investigate this mechanism through anomalous diffusion on anatomical brain networks, using the cat cortex as a representative example. We show that temporal nonlocality contracts the repertoire of weighted shortest communication paths, whereas spatial nonlocality expands it. Despite their opposite effects on path multiplicity, used here as a model-based proxy for functional connectivity, both regimes reduce geometric differentiation, as revealed by the intrinsic measures of GDT. A coupled model combining these mechanisms is embedded in a reversible anesthetic-burden model describing the progression from normal diffusion to maximum anesthetic effect and subsequent recovery. At maximum burden, regional and inter-region measures reveal a marked loss of differentiated and readable geometric information, which within GDT signifies loss of consciousness. Anesthetic clearance restores these measures to their normal values and re-establishes the geometric conditions for consciousness. Our results identify anesthetic-induced unconsciousness as a reversible collapse of neural propagation geometry.