Analytical or hybrid numerical-analytical solutions based on the Generalized Integral Transform Technique (GITT) are obtained for the transient three-dimensional pumping problem of aquifers with a fully penetrating vertical well between two parallel streams. The problem formulation for confined and leaky aquifers allows for achieving exact analytical solutions through integral transforms, while the unconfined aquifer case introduces a fourth kind boundary condition which leads to a coupled transformed head ordinary differential system, that can be solved either analytically or numerically. A convergence analysis is performed to illustrate the consistency of the numerical results achieved for the head distribution, as well as for the related pumping rates. Results are obtained for selected cases and comparisons with literature results are performed. A solution verification confirms the agreement of the integral transform solutions with available simulations and provides additional confidence for the analysis of a few physical parameters that influence the hydrological behavior.