To be on the safe side I would request the other institutions to fax over to Mayo all relevant tests, etc. Also take with you a list of all your tests with dates performed so that the new Doctor can see at a glance what tests have been performed and how recent they are. Include any conditions impacting when the tests were done.

I now have a long record at Mayo, and I can see that Doctors have difficulty in getting up to speed. So, when I went to see a new Doctor at Mayo last May, I wrote a one-page summary description of my current status, history of multiple related health issues, tests and procedures with dates, outcomes, etc. for the doctor. He actually used some of my writing in his notes.

I know Doctors can see info from linked institutions, because twice they have put something in their notes that came from outside and I had not had it forwarded. But I wonder how well organized it is and how it is displayed for the doctor.
I have observed that Mayo has made progress in designing their MyChart pages and reporting info in the last two years. You can actually compare test results including the ones from linked organizations.
I would like to see a clinical report summary for a complex patient which clearly indicates the patient's various diagnoses and critical data points. Right now, MyChart just lists conditions, including those from outside. Many are duplicates either because Mayo does not update my diagnosis (nodule vs. multiple nodules for example) or my local primary also adds it to my record.