B-cycle eMZVs have been defined in 1301.3042, and their properties are for instance discussed in 1803.00527, 1804.07989, and 1807.04506. We follow the conventions in section 2.2 of 1803.00527 for their normalization and relation to A-cycle eMZVs.
The expansion of B-cycle eMZVs around the cusp tau -> i infty is governed by a Laurent polynomial in tau which is referred to as their constant term in slight abuse of terminology.
The calculation of the constant terms of B-cycle eMZVs follows the method of the KZB associator as developed by Enriquez in 1301.3042 and reviewed in the appendix B of 1803.00527 (note two typos: in (B.7) the LHS should have exp(-\pi i t) rather than exp(\pi i t) and in (B.8) the factor exp(-2\pi i/tau e_+) should be exp(2\pi i/tau e_+))