Although many tools have been developed and employed to characterize temporal networks (TNs), the issue of how to compare them remains largely open. It depends indeed on what features are considered as relevant, and on the way the differences in these features are quantified. In this paper, we propose to characterize TNs through their behavior under general transformations that are local in time: (i) a local time shuffling, which destroys correlations at time scales smaller than a given scale b , while preserving large time scales, and (ii) a local temporal aggregation on time windows of length n . By varying b and n , we obtain a flow of TNs, and flows of observable values, which encode the phenomenology of the TN on multiple time scales. We use a symbolic approach to summarize these flows into labels (strings of characters) describing their trends. These labels can then be used to compare TNs, validate models, or identify groups of networks with similar labels. Our procedure can be applied to any TN and with an arbitrary set of observables, and we illustrate it on an ensemble of data sets describing face-to-face interactions in various contexts, including both empirical and synthetic data.