Identifying the existence or approval of a human in a number of past, recent and present day activities with the use of a handwritten signature is a captivating biometric challenge. Several engineering branches such as computer vision, pattern recognition and quite recently data-driven machine learning algorithms are combined in a multi-disciplined signature verification framework in order to deliver an equivalent and efficient e-assistance to manually executed duties, which usually demand knowledge and skills. In this work, we propose, for the first time, the use of a learnable Symmetric Positive Definite manifold distance framework in offline signature verification literature in order to build a global writer-independent signature verification classifier. The key building block of the framework relies on the use of regional covariance matrices of handwritten signature images as visual descriptors, which maps them into the Symmetric Positive Definite manifold. The learning and verification protocol explores both blind intra and blind inter transfer learning frameworks with the use of four popular signature datasets of Western and Asian origin. Experiments strongly indicate that the learnable SPD manifold similarity distance can be highly efficient for offline writer independent signature verification.