If you haveRead it straight: There is no overlap in practice. That is just a mismatched documentation which needs to be corrected.
You can leave out the exact dates if you'd want, while mentioning about experiences in future interviews, however if you have to explain, explain the same way you did here.
Also, your experience letter from Y will contain the actual date of joining, so there would be no overlapping, when you'll go for another company in future.