  Combining cosmological probes has consolidated the standard cosmological
model with percent precision, but some tensions have recently emerged when
certain parameters are estimated from the local or primordial Universe. The
origin of this behaviour is still under debate, however, it is crucial to study
as many probes as possible to cross-check the results with independent methods
and provide additional pieces of information to the cosmological puzzle. In
this work, by combining several late-Universe probes (0$<z<$10), namely, Type
Ia SuperNovae, Baryon Acoustic Oscillations, Cosmic Chronometers and Gamma-Ray
Bursts, we aim to derive cosmological constraints independently of local or
early-Universe anchors. To test the standard cosmological model and its various
extensions, considering an evolving Dark Energy Equation of State and the
curvature as a free parameter, we analyse each probe individually and all their
possible permutations. Assuming a flat $\Lambda$CDM model, the full combination
of probes provides $H_0=67.2^{+3.4}_{-3.2}$ km s$^{-1}$ Mpc$^{-1}$ and
$\Omega_m=0.325\pm0.015$ (68$\%$ C.L.). Considering a flat $w$CDM model, we
measure $w_0=-0.91^{+0.07}_{-0.08}$ (68$\%$ C.L.), while by relaxing the
flatness assumption ($\Lambda$CDM model, 95$\%$ C.L.) we obtain
$\Omega_k=0.125^{+0.167}_{-0.165}$. Finally, we analytically characterize the
degeneracy directions and the relative orientation of the probes' contours. By
calculating the Figure-of-Merit, we quantify the synergies among independent
methods, estimate the constraining power of each probe and identify which
provides the best contribution to the inference process. Pending the new
cosmological surveys, this study confirms the exigency for new emerging probes
in the landscape of modern cosmology.
