The broad line region (BLR) of Active Galactic Nuclei (AGN) contains the high velocity gas clouds transporting material from the dust torus to the accretion disk around the central super massive black hole (SMBH). Unveiling BLR structure is critical to understand the accretion mechanism driving the SMBH evolution and shaping the AGN inflows, outflows and jets. Reverberation Mapping (RM) constrains the BLR geometry, kinematic, mass and equivalent linear size with parameter degeneracies and fudge factors depending from the source geometry. Optical Interferometry (OI) yields independent constrains on BLR structure, mass and equivalent angular size. We developed a 3D geometrical model of BLRs to estimate both RM and OI measures and to show that the combination of these two techniques will very substantially reduce the uncertainty of mass estimates and yield direct distance measurement from quasar parallax. We used this model and a Monte Carlo Markov Chain Bayesian parameter fit of simulated data to show that quasar parallax can measure distances with accuracy better than 16%. We used it on actual data to interpret and explain our first OI observations of the BLR of the bright quasar 3C273 found to have a BLR of about 1750+/-35 light days (ld) much larger than predicted by RM (450+/-120 ld) and larger than the inner rim of the dust torus of about 800+/-270 ld, yielding a SMBH mass of (5+/-1) 10^8 solar masses. Our model and SNR computations show that the VLTI incoming instruments can observe about 60 BLRs covering more than 4 decades of luminosity, enough to try a grand unification of BLRs models and a calibration of RM making QSOs major cosmological probes.