Anisotropy in the magnetic fluctuation spectrum (stochastic anisotropy) and magnetic shear induce variations of global averaged quantities such as the running and the asymptotic diffusion tensors that can be investigated using a semi-analytical method. The study considers ranges for the anisotropy parameter, magnetic Kubo number and shear parameter leading to contrasting dynamical behaviors. In particular, the trapping of the stochastic magnetic field lines is analyzed. An asymptotic 'poloidal' velocity larger for stronger anisotropy is obtained for the wandering of the magnetic field lines for different values of the parameters.