We apply a persistent homology analysis to investigate the behavior of nanovoids during the crazing process of glassy polymers. We carry out a coarse-grained molecular dynamics simulation of the uniaxial deformation of an amorphous polymer and analyze the results with persistent homology. Persistent homology reveals the void coalescence during craze formation, and the results suggest that the yielding process is regarded as the percolation of nanovoids created by deformation.