  Among the thousands of exoplanets discovered to date, approximately a few
hundred gas giants on short-period orbits are classified as "lonely" and only a
few are in a multi-planet system with a smaller companion on a close orbit. The
processes that formed multi-planet systems hosting gas giants on close orbits
are poorly understood, and only a few examples of this kind of system have been
observed and well characterised. Within the contest of multi-planet system
hosting gas-giant on short orbits, we characterise TOI-1130 system by measuring
masses and orbital parameters. This is a 2-transiting planet system with a
Jupiter-like planet (c) on a 8.35 days orbit and a Neptune-like planet (b) on
an inner (4.07 days) orbit. Both planets show strong anti-correlated transit
timing variations (TTVs). Furthermore, radial velocity (RV) analysis showed an
additional linear trend, a possible hint of a non-transiting candidate planet
on a far outer orbit. Since 2019, extensive transit and radial velocity
observations of the TOI-1130 have been acquired using TESS and various
ground-based facilities. We present a new photo-dynamical analysis of all
available transit and RV data, with the addition of new CHEOPS and ASTEP+ data
that achieve the best precision to date on the planetary radii and masses and
on the timings of each transit. We were able to model interior structure of
planet b constraining the presence of a gaseous envelope of H/He, while it was
not possible to assess the possible water content. Furthermore, we analysed the
resonant state of the two transiting planets, and we found that they lie just
outside the resonant region. This could be the result of the tidal evolution
that the system underwent. We obtained both masses of the planets with a
precision less than 1.5%, and radii with a precision of about 1% and 3% for
planet b and c, respectively.
