Total (elastic + rotationally inelastic) integral cross sections are computed for O(2)((3)Sigma(-)(g))-O(2)((3)Sigma(-)(g)) using a recent ab initio potential energy surface. The sampled velocity range allows us a thorough comparison of the glory interference pattern observed in molecular beam experiments. The computed cross sections are about 10% smaller than the measured ones, however, a remarkable agreement in the velocity positions of the glory extrema is achieved. By comparing with models where the anisotropy of the interaction is reduced or removed, it is found that the glory pattern is very sensitive to the anisotropy, especially the positions of the glory extrema. (C) 2011 Elsevier B. V. All rights reserved.