Relative localization is a crucial functional block of any robotic swarm. We address it in a fleet of nano-drones characterized by a 10 cm-scale form factor, which makes them highly versatile but also strictly limited in their onboard power envelope. State-of-the-Art solutions leverage Ultra-WideBand (UWB) technology, allowing distance range measurements between peer nano-drones and a stationary infrastructure of multiple UWB anchors. Therefore, we propose an UWB-based infrastructure-free nano-drones swarm, where part of the fleet acts as dynamic anchors, i.e., anchor-drones (ADs), capable of automatic deployment and landing. By varying the Ads' position constraint, we develop three alternative solutions with different trade-offs between flexibility and localization accuracy. In-field results, with four flying mission-drones (MDs), show a localization root mean square error (RMSE) spanning from 15.3 cm to 27.8 cm, at most. Scaling the number of MDs from 4 to 8, the RMSE marginally increases, i.e., less than 10 cm at most. The power consumption of the MDs' UWB module amounts to 342 mW. Ultimately, compared to a fixed-infrastructure commercial solution, our infrastructure-free system can be deployed anywhere and rapidly by taking 5.7 s to self-localize 4 ADs with a localization RMSE of up to 12.3% in the most challenging case with 8 MDs.