Quasi-spherical and Keplerian disk accretion scenarios encounter difficulties explaining the origin and observed spin evolution of long-period X-ray pulsars. These difficulties reflect an oversimplification of the scenarios in which the magnetic field of the accretion flow is neglected. The accretion picture onto a neutron star which captures material from a magnetized wind differs from those previously suggested. It can be explained in terms of a dense non-Keplerian magnetic disk in which the material is confined by its intrinsic magnetic field. This scenario (a so called Magnetic-Levitation Accretion) is actively investigated for the case of a black hole for more than 40 years but has been applied to the case of a neutron star only recently. I show that a neutron star accreting material from the magnetically-levitating disk (MAGLEV-disk) brakes harder and the radius of its magnetosphere is significantly smaller than that evaluated in the traditional non-magnetic accretion flow scenarios. The mass-transfer towards the neutron star in MLA scenario is governed by anomalous diffusion and the expected appearance of the MLA pulsar are in a good agreement with observations.