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Accurate real-time catheter segmentation is an important pre-requisite for robot-assisted endovascular intervention. Most of the existing learning-based methods for catheter segmentation and tracking are only trained on small-scale datasets or synthetic data due to the difficulties of ground-truth annotation. Furthermore, the temporal continuity in intraoperative imaging sequences is not fully utilised. In this paper, we present FW-Net, an end-to-end and real-time deep learning framework for endovascular intervention. The proposed FW-Net has three modules: a segmentation network with encoder-decoder architecture, a flow network to extract optical flow information, and a novel flow-guided warping function to learn the frame-to-frame temporal continuity. We show that by effectively learning temporal continuity, the network can successfully segment and track the catheters in real-time sequences using only raw ground-truth for training. Detailed validation results confirm that our FW-Net outperforms state-of-the-art techniques while achieving real-time performance.