The astrophysics field of compact binary millisecond pulsars is thriving. This growing class of rapidly spinning neutron stars – also known as "spiders"– constitutes the most promising place to find massive pulsars. Super-massive neutron stars, with a mass significantly higher than two Solar masses, cannot contain exotic particles. Finding such stars would have profound implications for nuclear physics. The maximum neutron star mass has also important consequences for the fate of supernovae and the gravitational wave signal from neutron star mergers. In addition, spiders offer a unique probe of the pulsar's innermost wind and a nearby site for particle acceleration. The past years have seen exciting discoveries in this field, in which I have been closely involved. As a result, a new way has opened up to study fundamental astrophysical phenomena from compact binary millisecond pulsars. The purpose of this project is to find the most massive neutron stars and to understand the interaction between accretion flows, pulsar winds and neutron star magnetospheres. LOVE-NEST will first uncover a hidden population of millisecond pulsars, with a targeted search of gamma-ray candidate sources. We will then measure accurately the masses of the heaviest pulsars, using a novel technique that we have recently established. We will also investigate nearby spiders as potential sources of cosmic rays and astrophysical neutrinos, placing unprecedented constraints on particle acceleration in relativistic pulsar wind shocks. LOVE-NEST will have a strong impact on gravitational wave astronomy, nuclear physics, astrophysics and astro-particle physics. As a leader in the field, and having developed a new method to measure pulsar masses, I am in an excellent position to achieve these ambitious goals.