The ring species conundrum
As commented above, in essence this is the classic case study of ring species, and reading up on it will completely answer your question. A case of ring species is visualizable geographically (area A, area B, area C, and 'variant species' graduating across).
'Transitive', jargon and the idea of transition
Sure, something's transitive if A is B, and B is C, and it follows that A is C. But species are not transitive sets (of numbers). It's a bit along the lines of 'mixing'. Say, by analogy, if water dissolves soap, and soap dissolves fat, it does not mean that water dissolves fat. I wouldn't use mathematical terminology in biology (i.e. I would also not call species intransitive or nontransitive, it would not be helpful) but I would rather focus on the concept and word "transition". Lineages evolve and diverge gradually, some remain extant and co-exist with- and sometimes without interbreeding. I think lineages you can talk about in a very robust manner in the long term. The 'species' category is more about 'binning', deciding which section or degree of branching of the lineage you want to consider a unit.
Imagine the concept phylogenetically
Extant (currently living) canines are a nice example. Those similar can interbreed naturally, those dissimilar cannot realistically or even physically or genetically interbreed. Chihuahuas and wolfhounds or Great Danes could be construed as different species with our classical definition of species, because they truly do not interbreed. Yet they are widely and scientifically today considered the same species! You can surmise that there is difficulty with this classical concept of using 'species', when used stringently and in a strictly categorical fashion... let's consider it from another point of view...
Imagine the concept though time
If one's ancestors 5 generations back could interbreed with ancestors 10 generations ago, we could 'define' them as a species. Perhaps even those 5 and 1,000 generations back. What about 10,000? What about 100,000? 100,000,000,000? You see, every generation can interbreed with the next, yet at some point we choose to categorize them as different species. You have to understand that we define biological species not because there is such a real thing as a species boundary, but only because it helps us think about things by chunking them arbitrarily together. The concept of species is useful, but not objectively a feature in reality.
I would also refer you to my previous answer on what the definition of a species is and why it's always been problematic. I think that will help with a more complete understanding.