Transitive means that if A is related to B in some way, and B is related to C in at least the same way, then A is related to C in at least that same way. They may have other relationships as well, but those must apply. Transitive closure is the operation of adding links between entities to make the resulting network transitive, or the result of doing so.
This website is concerned with the relationship of ownership. If person A owns some legal entity B, and B owns some legal entity C, then A does in fact own C, regardless of the wording of contracts between them. Some other relationship, like being located in the same city may also hold true, but here we are only concerned with ownership.
With ownership comes responsibility. If ownership is transitive, then A shares responsibility for damages caused by C, even if some contractual wording has been put in place to spare A any responsibility for the actions of the company C.
In general, people who own things who own things do not like this idea.
I think it is the same kind of idea as that of corporate personhood or citizenship, as in the notorious Citizens United ruling. But whereas that was popular with rich people, this idea would horrify them.
This domain name, TransitiveOwnership.org currently points to a subdomain of MigrationPlans.com — though it represents one of the most difficult social migration problems of all.