Full Idea
When the identity relation is vague, it may seem intransitive; a claim of apparent identity may yield an apparent non-identity. Some sort of 'counterpart' notion may have some utility here.
Gist of Idea
A vague identity may seem intransitive, and we might want to talk of 'counterparts'
Source
Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 18)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.51
A Reaction
He firmly rejects the full Lewis apparatus of counterparts. The idea would be that a river at different times had counterpart relations, not strict identity. I like the word 'same' for this situation. Most worldly 'identity' is intransitive.