Visualizing time-varying data defined on the nodes of a graph is a challenging problem that has been faced with different approaches. Although techniques based on aggregation, topology, and topic modeling have proven their usefulness, the visual analysis of smooth and/or abrupt data variations as well as the evolution of such variations over time are aspects not properly tackled by existing methods. In this work we propose a novel visualization methodology that relies on graph wavelet theory and stacked graph metaphor to enable the visual analysis of time-varying data defined on the nodes of a graph. The proposed method is able to identify regions where data presents abrupt and mild spacial and/or temporal variation while still been able to show how such changes evolve over time, making the identification of events an easier task. The usefulness of our approach is shown through a set of results using synthetic as well as a real data set involving taxi trips in downtown Manhattan. The methodology was able to reveal interesting phenomena and events such as the identification of specific locations with abrupt variation in the number of taxi pickups.