  Persistent homology and zigzag persistent homology are techniques which track
the homology over a sequence of spaces, outputting a set of intervals
corresponding to birth and death times of homological features in the sequence.
This paper presents a method for choosing a homology class to correspond to
each of the intervals at each time point. For each homology class a specific
representative cycle is stored, with the choice of homology class and
representative cycle being both geometrically relevant and compatible with the
birth-death interval decomposition. After describing the method in detail and
proving its correctness, we illustrate the utility of the method by applying it
to the study of coverage holes in time-varying sensor networks.
