The Gaia EDR3, Gaia DR2 and Gaia DR1 catalogues are formally independent. This means a direct one-to-one correspondence between the source identifiers from Gaia DR2 and Gaia DR3 is not guaranteed. That is, the same physical object might have different source_id in each release. Having the same numerical identifier in both catalogues does also not necessarily mean they refer to the same astronomical object. Further details on the pre-processing cross-match can be found in Section 3.4.13.
This means deciding which sources in different data releases might be physically related is a scientific problem on its own, where all the evidence at hand must be carefully considered. Hence, best neighbour pairs have not been determined. However, a helper table has been created to facilitate scientific exploitation. It contains the results of a cone search between all objects in Gaia DR2 and Gaia EDR3. Proper motion correction has been applied to Gaia EDR3, when possible, due to the higher completeness and quality of its astrometry.