  3D maps of the extinction density in the Galaxy can be built through the
inversion of catalogues of distance-extinction pairs for individual target
stars. The spatial resolution of the maps that can be achieved increases with
the spatial density of the targets, and subsequently with the combination of
catalogues. However, this requires their careful inter-calibration. Our aim is
to develop methods of inter-calibration of two different catalogues. We used as
reference a spectrophotometric catalogue. A principal component analysis was
performed in G,GB,GR,J,H,K multi-colour space for the second catalog. The
subspace constituted by the two first components was split into cells in which
we estimated deviations from the reference. The deviations were computed using
all targets from the reference located at a short spatial distance of each
secondary target. Corrections and filtering were deduced for each cell in the
multi-colour space. We applied the technique to two different datasets: on the
one hand, the spectrophotometric catalogue, and, on the other hand, a catalogue
of extinctions based on photometry of Gaia eDR3 and 2MASS. After calibration,
the dispersion of the extinction among neighbouring points in the second
catalogue is reduced, regardless of whether reference targets are present
locally. Weak structures are then more apparent. The extinction of high
Galactic latitude targets is more tightly correlated with the dust emission, a
property acquired from the first catalogue. A hierarchical inversion technique
was applied to the two merged inter-calibrated catalogues to produce 3D
extinction density maps corresponding to different volumes and maximum spatial
resolution. The maximum resolution is 10pc for a 3000x3000x800pc3 volume around
the Sun, and the maximum size of the maps is 10x10x0.8 kpc3 for a resolution of
50pc. Maps can be downloaded or used by means of on-line tools.
