Left Ventricular Assist Devices (LVADs) are increasingly used as long-term implantation therapy for advanced heart failure patients, a situation in which candidacy assessment is crucial for successful treatment and recovery. A deep learning system based on Electrocardiogram (ECG) data and trained with multiple publicly available datasets in an inter-patient paradigm is proposed, where each diagnosis of interest has observations from at least two datasets to increase generalizability. The proposed system consists of three main parts: a single-lead classifier, a 12- lead classifier, and a semantic segmentation classifier, achieving state-of-the-art results on the classification evaluation of each model, with multilabel average AUC results of 0.9924, 0.9468, and 0.9956, respectively. The proposed ECG diagnosis criteria are divided into three groups: major criteria, minor criteria, and potential contraindications. The identification of the relevant ECG diagnoses and the validation of the proposed criteria were performed with expert input. The output is the estimated probability of having each one of these diagnoses, and no single numerical score is proposed as a final measure of candidacy. Instead, a more informative report is proposed to increase the trust and applicability of the system. A results report of the predicted probability of the diagnoses in non-binary language according to the probability bin (e.g., cannot rule out, possible, consistent with) is proposed as output to the physician, along with per-lead interpretability capability given by Grad-CAM implementation in the multi-head model, and box-plots per diagnosis that show the predicted probability and its uncertainty estimation obtained with Monte Carlo Dropout. Overall, this work presents a novel approach to LVAD candidacy assessment using deep learning based on ECG diagnosis criteria. The proposed system achieves state-of-the-art results and provides interpretability and awareness of uncertainty, increasing the trust and applicability of the system in real-world healthcare applications.