Supporting user interactivity in peer-to-peer streaming systems is challenging. VCR-like operations, such as random seek, pause, fast forward and rewind, require timely P2P overlay topology adjustment and appropriate bandwidth resource re-allocation. If not handled properly, the dynamics caused by user interactivity may severely deteriorate users' perceived video quality, e.g., longer start-up delay, frequent playback freezing, or blackout altogether. In this paper, we propose a derivative tree-based overlay management scheme to support user interactivity in P2P streaming system. Derivative tree takes advantage of well organized buffer overlapping to support asynchronous user requests while brings high resilience to the impact of VCR-like operations. A session discovery service is introduced to quickly locate parent peer. We show that the overhead of VCR-like operations in derivative-tree based scheme is O(log(N)), where N is the number of sessions. Simulation experiments further demonstrate the efficiency of the proposed scheme.