Objective: This paper tackles the problem of transfer learning in the context of EEG-based Brain Computer Interface (BCI) classification. In particular the problems of cross-session and cross-subject classification are considered. These problems concern the ability to use data from previous sessions or from a database of past users to calibrate and initialize the classifier, allowing a calibration-less BCI mode of operation. Methods: Data are represented using spatial covariance matrices of the EEG signals, exploiting the recent successful techniques based on the Riemannian geometry of the manifold of Symmetric Positive Definite (SPD) matrices. Cross-session and cross-subject classification can be difficult, due to the many changes intervening between sessions and between subjects, including physiological , environmental, as well as instrumental changes. Here we propose to affine transform the covariance matrices of every session/subject in order to center them with respect to a reference covariance matrix, making data from different sessions/subjects comparable. Then, classification is performed both using a standard Minimum Distance to Mean (MDM) classifier, and through a probabilistic classifier recently developed in the literature, based on a density function (mixture of Riemannian Gaussian distributions) defined on the SPD manifold. Results: The improvements in terms of classification performances achieved by introducing the affine transformation are documented with the analysis of two BCI data sets. Conclusion and significance: Hence, we make, through the affine transformation proposed, data from different sessions and subject comparable, providing a significant improvement in the BCI transfer learning problem.