We propose an effective model to describe the bias induced on cosmological observables by
Laniakea, the gravitational supercluster hosting the Milky Way, which was defined using peculiar
velocity data from Cosmicflows-4 (CF4). The structure is well described by an ellipsoidal shape
exhibiting triaxial expansion, reasonably approximated by a constant expansion rate along the
principal axes. Our best fits suggest that the ellipsoid, after subtracting the background
expansion, contracts along the two smaller axes and expands along the longest one, predicting an
average expansion of ∼ -1.1 km/s/Mpc. The different expansion rates within
the region, relative to the mean cosmological expansion, induce line-of-sight-dependent
corrections in the computation of luminosity distances. We apply these corrections to two
low-redshift datasets: the Pantheon+ catalog of type Ia Supernovae (SN Ia), and 63 measurements of
Surface Brightness Fluctuations (SBF) of early-type massive galaxies from the MASSIVE survey. We
find corrections on the distances of order ∼ 2-3%, resulting in a shift in the inferred
best-fit values of the Hubble constant H
0 of order ΔH
0
SN Ia ≈ 0.5 km/s/Mpc and ΔH
0
SBF ≈ 1.1 km/s/Mpc,
seemingly worsening the Hubble tension.