Neutron stars, the most compact stars in the Universe, have a mass density larger than nuclear mass density, which cannot be achieved in laboratory conditions and their property and composition are still to be clarified and remain puzzling objects after several decades from their first observations. The size and mass of a neutron star depends on its unknown composition, or on the equation of State of the matter it is composed of: studies of neutron stars are important for astrophysics and nuclear and elementary particle physics. However the inner core of a neutron star can be probed via gravitational waves as once emitted, they travel through space and matter with negligible interaction. For instance a phase transition in the star core may occur during its evolution, as rotation stows down and the central pressure increases due to the reduction of centrifugal forces with different nuclear matter states that can be almost degenerate, like e.g. matter with hyperons, bose condensates with properties of $\pi$ or $K$-mesons, deconfined quark matter. Such phase transitions lead to starquakes, with consequent release of gravitational and electromagnetic waves (and possibly neutrinos). Particular interests assume the emitted gravitational waves, as their frequency contains information to possibly discriminate between different equation of State. In our galaxy we know about the presence of many NS via their electromagnetic emission, for which the time evolution of the rotation period has been tracked over years. For few targeted pulsars, it is also known the occurrence of erratic glitches which change discontinuously the rotation period, which are possibly, even though not exclusively, associated with the above mentioned phase transitions. Since it is expected that many more neutron stars are expected to exist in our galaxy, just not visible to us as their focused electromagnetic emission is not pointing to us, we plan to use the known information about galactic neutron star population (distribution of time period) with the information we have about glitch rates of well-followed NS in order to estimate the amount of phase transition happening in the NS populations. Even in case of persistent non-observation of gravitational wave bursts, this can be used to set non-trivial upper bounds on the amount of gravitational wave emitted and/or to constrain the kind of equation of states the NS have to fulfill. (AU)