agramfort/mne-python — comment on commit 0c22e6093c8ba04d800ec856e3363b3d13c257a0
File:  line 0
By mluessi:

Well, since we already subtracted the mean when computing each covariance, it is still not 100% correct but should be close assuming we have enough samples and the mean in both segments is the same.

I think the really correct solution would be to also store E[XX^T] and E[X]E[X]^T in the covariance object, since the covariance is given by

cov(X) = E[XX^T] - E[X]E[X]^T

we could also rescale E[X]E[X]^T when "adding covariances". But this would make things more complicated and break comparability with MNE..