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Ischemic strokes are often caused by large vessel occlusions (LVOs), which can be visualized and diagnosed with Computed Tomography Angiography scans. As time is brain, a fast, accurate and automated diagnosis of these scans is desirable. Human readers compare the left and right hemispheres in their assessment of strokes. A large training data set is required for a standard deep learning-based model to learn this strategy from data. As labeled medical data in this field is rare, other approaches need to be developed. To both include the prior knowledge of side comparison and increase the amount of training data, we propose an augmentation method that generates artificial training samples by recombining vessel tree segmentations of the hemispheres or hemisphere subregions from different patients. The subregions cover vessels commonly affected by LVOs, namely the internal carotid artery (ICA) and middle cerebral artery (MCA). In line with the augmentation scheme, we use a 3D-DenseNet fed with task-specific input, fostering a side-by-side comparison between the hemispheres. Furthermore, we propose an extension of that architecture to process the individual hemisphere subregions. All configurations predict the presence of an LVO, its side, and the affected subregion. We show the effect of recombination as an augmentation strategy in a 5-fold cross validated ablation study. We enhanced the AUC for patient-wise classification regarding the presence of an LVO of all investigated architectures. For one variant, the proposed method improved the AUC from 0.73 without augmentation to 0.89. The best configuration detects LVOs with an AUC of 0.91, LVOs in the ICA with an AUC of 0.96, and in the MCA with 0.91 while accurately predicting the affected side.