Is potential causality relation equals to set of consistent happens before relations?
The book says "A potential causality diagram is equivalent to the set of happened before diagrams that are consistent with it."  (emphasis added)

You seem to have interpreted that as "A potential causality diagram is equal to the union of happened before diagrams that are consistent with it."  But that's not the same statement.  I would suspect that this might be the cause of your confusion.  Go back to the original statement and disregard the idea of taking the union, and see if you can make sense of the original statement.

Perhaps there is additional explanation or context after that sentence.

If not, perhaps the book is claiming there is a bijection between (a causality diagram C) and (the set of happens-before relations that are consistent with C).  That claim sounds accurate.  To construct the inverse map: given such a set of happens-before relations, take the smallest element in the set, and that's C.