Figure 3

Several examples showing how the zigzag persistence diagram can be affected by the existence of small loops. The first and third; and the second and fourth examples have the same filtration with the addition of a single triangle in the later case. In each case, the generators of homology are shown with the interval decomposition drawn below. The resulting persistence diagrams show that the third and fourth examples show a single bar representing the persisting loop. However in the first two intervals are quite different, where the long lived bar is split into two pieces in the second example