A 3D tracking of individual bubbles in bubble swarms is essential for revealing and understanding bubble interactions and clustering mechanisms in bubbly flows. In this work, we address this issue and present a new method for tracking deformable bubbles in 3D based on deep learning models. We also present a new dataset of artificial bubbly flow sequences to test the tracker, which could also be used to train future detection or tracking models. Although the developed tracker had difficulties in cases with a large number of bubbles, it showed an overall good performance on the complete dataset and demonstrates the potential of deep learning models for this task. We hope that this work fosters further developments as well as applications of 3D bubble tracking that at the end lead to a deeper understanding of how deformable bubbles interact.