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The cooperation of a human pilot with an autonomous agent during flight control realizes parallel autonomy. A parallel-autonomous system acts as a guardian that significantly enhances the robustness and safety of flight operations in challenging circumstances. Here, we propose an air-guardian concept that facilitates cooperation between an artificial pilot agent and a parallel end-to-end neural control system. Our vision-based air-guardian system combines a causal continuous-depth neural network model with a cooperation layer to enable parallel autonomy between a pilot agent and a control system based on perceived differences in their attention profile. The attention profiles are obtained by computing the networks' saliency maps (feature importance) through the VisualBackProp algorithm. The guardian agent is trained via reinforcement learning in a fixed-wing aircraft simulated environment. When the attention profile of the pilot and guardian agents align, the pilot makes control decisions. If the attention map of the pilot and the guardian do not align, the air-guardian makes interventions and takes over the control of the aircraft. We show that our attention-based air-guardian system can balance the trade-off between its level of involvement in the flight and the pilot's expertise and attention. We demonstrate the effectivness of our methods in simulated flight scenarios with a fixed-wing aircraft and on a real drone platform.