This paper presents an innovative and generic deep learning approach to monitor heart conditions from ECG signals.We focus our attention on both the detection and classification of abnormal heartbeats, known as arrhythmia. We strongly insist on generalization throughout the construction of a deep-learning model that turns out to be effective for new unseen patient. The novelty of our approach relies on the use of topological data analysis as basis of our multichannel architecture, to diminish the bias due to individual differences. We show that our structure reaches the performances of the state-of-the-art methods regarding arrhythmia detection and classification.