This paper treats the safety issues in coordinated transportation of an object via multiple Unmanned Aerial Vehicles with Manipulator Systems (UAVMS); in particular, the case of obstacle avoidance is considered. The proposed paradigm is based on the so-called Null-Space-based Behavioral (NSB) control approach, that allows to achieve multiple tasks simultaneously. Two different scenarios of bar transportation using multi-UAVMSs have been developed, tested and compared in simulation: in the first scenario, the obstacle avoidance is achieved at the coordination level, where the controller allows the whole system (UAVMSs and bar) to circumnavigate the obstacle; while in the second scenario only the UAVMS closest to the obstacle modifies its trajectory to overcome the obstacle by keeping the desired trajectory of the bar unchanged.