Transitions are base mutations of purine to purine (A <-> G) or pyrimidine to pyrimidine (C <-> T). Transversions are purine to pyrimidine or vice versa (A <-> C, A <-> T, G <-> C, G <-> T). And it is well-known that transitions are more common than transversions in the populations.
So what is the condition in the evolution of duplicated genes? Suppose a gene A is duplicated with two copies A1 and A2 in the same genome (not two alleles in different sets of chromosomes, or the same gene in two different cells/organisms). At first A1 and A2 had the same sequence, but then they went through an evolution process and each got some mutations. Now let's check the sequence of A1 and A2 again, are the differences between A1 and A2 mainly transitions instead of transversions?
Although I think it would not be surprising to find that transitions are more common in this condition, I've searched some papers focusing on the evolution of duplicated genes to look for some support. However, they mainly discuss what happened to their functions instead of sequences.