In this MHD-model of the heliosphere, we assume a Parker-type flow, and a Parker-type spiral magnetic field, which is extrapolated further downstream from the termination shock to the heliopause. We raise the question whether the heliopause nose region may be leaky with respect to fields and plasmas due to non-ideal plasma dynamics, implying a breakdown of the magnetic barrier. We analyse some simple scenarios to find reconnection rates and circumstances, under which the heliosphere can be an “open” or a “closed” magnetosphere. We do not pretend to offer a complete solution for the heliosphere, on the basis of non-ideal MHD theory, but present a prescription to find such a solution on the basis of potential fields including the knowledge of neutral points. As an example, we imitate the Parker-spiral as a monopole with a superposition of homogeneous asymptotical boundary conditions. We use this toy model for x<−R, where R=100AU is the distance of the termination shock to describe the situation in the nose region of the heliopause.