Jean-Baptiste
I am a planner with Cambridge, MA, one of the cities in the Boston Metro region. Information on PUMA boundaries and which PUMAs are included in a region is harder to locate than you would expect.
One trick you can use is to go to the IPUMS USA website, which is a University of Minnesota program that enables on-line analysis of PUMS data.
https://usa.ipums.org/usa/index.shtml
You will need to set up an account to use the on-line analysis tools.
You can run a simple analysis on IPUMS USA that generates a list of Boston MSA PUMAs as a byproduct. For example, if you filter for the Boston MSA using msa2013(14460) and ask for a count of all cases by PUMA by sex you will get a list of PUMAs. (I am trying to upload the list as a file to the ACS Data users Group but am running into problems.) I can tell this is likely the correct list by comparing the sum of PUMA populations to the ACS population for the region.
One thing to be aware of is that PUMAs were renumbered following the 2010 US Census. I believe that ACS data issued prior to 2012 use the older different numbering system and data sets that cross that date use both sets of PUMA numbers. For example, Cambridge, MA is now PUMA 0506 and previously was PUMA 3200. I also believe that PUMA numbers can be repeated between states, but I could be wrong about this.
You can find PUMA reference maps here:
https://www.census.gov/geographies/reference-maps/2010/geo/2010-pumas.html
Note that the Boston MSA extends into New Hampshire. You can see a map of MSAs here:
https://www2.census.gov/geo/maps/metroarea/us_wall/Sep2018/CBSA_WallMap_Sep2018.pdf?#
I hope this is helpful.