Cardiovascular disease treatment involves the challenging task of navigating guidewires and catheters through the vascular anatomy. This often results in prolonged procedures where both the patient and clinician are subjected to X-ray radiation. As a potential solution, Deep Reinforcement Learning methods have demonstrated potential in learning this task, paving the way for automated catheter navigation during robotic interventions. However, current works show a limited ability to generalize to unseen and/or deforming anatomies. In this paper, we extend our previous reinforcement learning approach in two main areas: we improve the training strategy to learn a control of the device even when the vascular anatomy is deforming and we propose a method to estimate the motion of the anatomy from single view fluoroscopy images. The combination of these two contributions makes it possible to automatically navigate across a moving vascular anatomy under fluoroscopic imaging, even without injecting a contrast agent. We validate our method on two scenarios: a simulated beating heart and a liver subjected to breathing motion. Our approach leads to an average success rate of 95% in reaching random targets within these anatomies. Our framework is also computationally efficient, enabling the training of our controller to be completed in about 6 hours.