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We focus in this paper on Internet flows, consider their contributions to the overall traffic per time unit or bin, and perform a multi-scale and multi-protocol analysis to explore the persistency properties of those flows that contribute the most (also known as "heavy hitters" or "elephants"). Knowing the persistency features (or a lack thereof) of the heavy hitters and understanding their underlying causes is crucial when developing traffic engineering tools that focus primarily on optimizing system performance for elephant flows.The main difficulty when studying the persistency properties of flows is that the available measurements are either too fine-grained to perform large-scale studies (i.e., packet-level traces) or too coarse-grained to extract the detailed information necessary for the purpose at hand (i.e., Netflow traces, SNMP). We deal with this problem by assuming that flows have constant throughput through their lifetime. We then check the validity of this assumption by comparing our Netflow-derived findings against those obtained from directly studying the corresponding detailed packet-level traces. By considering different time aggregations (e.g., bin sizes between 1--10 minutes) and flow abstractions (e.g., raw IP flows, pre-fix flows), varying the definition of what constitutes an "elephant", and slicing by different protocols and applications, we present a methodology for studying persistency aspects exhibited by Internet flows. For example, we find that raw IP flows that are elephant flows for at least once (i.e., one bin or time unit) in their lifetimes tend to show a remarkable persistence to be elephants for much of their lifetimes, but certain aggregate flows exhibit more intricate persistency properties.