Abstract : Multi Object Adaptive Optics (MOAO) is a solution developed to perform a correction by adaptive optics (AO) in a science large field of view. As many wide field AO scheme, a tomographic reconstruction of the turbulent volume is required in order to compute the MOAO corrections to be applied in the dedicated directions of the observed very faint targets. The specificity of MOAO is the open loop control of the deformable mirrors by a number of the wavefront sensors which are coupled to bright guide stars in different directions. MOAO calls for new procedures both for the cross registration of all the channels and for the computation of the tomographic reconstructor. The proposed approach, called Learn and Apply (L&A), allows us to retrieve the tomographic reconstructor using the on-sky wavefront measurements from an MOAO instrument. This method is also used to calibrate the registrations between the off-axis wavefront sensors and the deformable mirrors placed in the science optical paths. The procedure links the WFSs in the different directions and measures directly on-sky the required covariance matrices needed for the reconstructor. The theoretical expressions of the turbulence spatial covariance of wavefront slopes allows to derive any turbulent covariance matrix between two wavefront sensors. It is discussed the convergence issue on the measured covariance matrices, and proposed the fitting of the data based on the theoretical slope covariance using a reduced number of turbulence parameters. The Learn and Apply tomography method has been fully tested and validated in laboratory, on the SESAME bench, and will be tested on-sky, on the MOAO demonstrator called CANARY installed in 2010 at the William Herschel Telescope (Canaries Islands).