Bittorrent is one of the most popular and successful applications in the current Internet. However, we still have little knowledge about the topology of real Bittorrent swarms, how dynamic the topology is, and how it affects overall behavior. This paper describes an experimental study of the overlay topologies of real-world Bittorrent networks, focusing on the activity of the nodes of its P2P topology and especially their dynamic relationships. Peer Exchange Protocol (PEX) messages are analyzed to infer topologies and their properties, capturing the variations of their behavior. Our measurements, verified using the Kolmogorov-Smirnov goodness of fit test and the likelihood ratio test and confirmed via simulation, show that a power-law with exponential cutoff is a more plausible model than a pure power-law distribution. We also found that the average clustering coefficient is very low, supporting this observation. Bittorrent swarms are far more dynamic than has been recognized previously, potentially impacting attempts to optimize the performance of the system as well as the accuracy of simulations and analyses.