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Visual monitoring operations underwater require both observing in close-proximity the objects of interest, and tracking the few feature-rich areas necessary for state estimation. This paper introduces the first navigation framework, called AquaVis, that produces on-line visibility-aware motion plans that enable Autonomous Underwater Vehicles (AUVs), to track multiple visual objectives with an arbitrary camera configuration in real-time. Using the proposed pipeline, AUVs can efficiently move in 3D, reach their goals while avoiding obstacles safely, and maximizing the visibility of multiple objectives along the path within a specified proximity. The method is sufficiently fast to be executed in real-time and is suitable for single or multiple camera configurations. Experimental results show the significant improvement on tracking multiple automatically-extracted points of interest, with low computational overhead and fast re-planning times.