Did any of the Anastasi people come to America? If so, American documents may be found. Do you have any particular Anastasi in mind? if so, maybe you can provide name, birth information, as well as names other family members. If there are brothers and sisters, you could mention those names. Ship records will tell the area of where the people came from.
Also, if you have any idea of what Italian town they came from, please mention. Having this type of information will let others who help from this forum help you better.
Anastasi is a base uitalian surname from which allother variations emanate. It appears in the italian surname dictionary. If you go to www.google.com and insert Anastasi and genealogy alongside in the title all researches on the naame being done or completed will appear. The hometown may be on micorfilm at the family history library which you did not mention in your inquiry. Peter