Dear Su Perullo
Thank you for contacting History Hub.
Because your family resided in Massachusetts, we suggest that you contact the staff at the National Archives at Boston via email firstname.lastname@example.org to have them perform a search through the naturalization records they maintain from the Federal courts in that area. Please be sure to provide all known name variants in your request to allow for a successful search.
You may also want to consult this microfilm publication, which is at the National Archives at Boston:
M1299. Index to New England Naturalization Records, 1791-1906 (117 rolls). NAID 4498967. This serves a similar function for naturalizations occurring in various courts in the six New England States of Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont.
National Archives Catalog: https://catalog.archives.gov/id/4498967
Here is a roll list: https://www.archives.gov/files/research/microfilm/m1299.pdf
Unfortunately, it does not appear that there is a digital copy available on the NARA Catalog.
The National Archives at Boston also has four other microfilm series involving passenger arrivals, but the earliest of these dates to 1895, which is later than your request of 1870s.
For more information concerning our immigration holdings please
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RRPO (The National Archives at St. Louis). Also, NPRC will continue servicing requests ONLY associated with medical treatments, burials, and homeless veterans seeking admittance to a homeless shelter. If your request is urgent, please see Emergency Requests and Deadlines. Please refrain from submitting non-emergency requests such as replacement medals, administrative corrections, or records research until NPRC returns to pre-COVID staffing levels. Please check archives.gov/veterans for updates to the NPRC operating hours and status. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this is helpful. Best of luck in your research.