quantum field theory - Significance of total divergence anomaly term

What is the significance of the fact that the anomany term (calculated from the triangle diagram) is a total divergence? Or, in other words, what is the significance of

$$\partial_\mu j^\mu_A\sim Tr(W\tilde{W}) =\text{a total divergence}$$ for global anomalies. I think this fact is related to why baryon number violation in standard model cannot be a perturbative process. Perhaps someone can illuminate.