In this paper, we propose an enhanced CNN model for detecting supernovae (SNe). This is done by applying a new method for obtaining rotational invariance that exploits cyclic symmetry. In addition, we use a visualization approach, the layer-wise relevance propagation (LRP) method, which allows finding the relevant pixels in each image that contribute to discriminate between SN candidates and artifacts. We introduce a measure to assess quantitatively the effect of the rotational invariant methods on the LRP relevance heatmaps. This allows comparing the proposed method, CAP, with the original Deep-HiTS model. The results show that the enhanced method presents an augmented capacity for achieving rotational invariance with respect to the original model. An ensemble of CAP models obtained the best results so far on the HiTS dataset, reaching an average accuracy of 99.53%. The improvement over Deep-HiTS is significant both statistically and in practice.