You can find all of the resources that IPUMS provides to help with PUMA correspondences through the IPUMS USA Geographic Tools and Resources page.
There are tract correspondence files only for 2020, 2010, and 1960 PUMAs.
For 1990 and 2000 PUMAs, official PUMA definitions were based not only on tracts and counties, but also commonly on county subdivisions and places, areas that need not align with tract boundaries. As such, the composition files for 1990 and 2000 PUMAs include a mixture of county, tract, county subdivision, and place component parts.
The 1980 “county groups” often subdivide counties, making them more like PUMAs than true groups of counties. But they don’t officially correspond to sets of tracts. Rather, they may correspond to sets of counties, minor civil divisions (i.e., county subdivisions that are legally defined), or places, or the parts of counties not included in places.
1970 county groups almost universally do correspond to sets of one or more counties, except in Hawaii.
1960 PUMAs were created by IPUMS USA to correspond approximately to 2000 PUMAs, building up from 1960 tracts and counties. This is why we provide a composition file for 1960 PUMAs based on tracts and counties, as well as a relationship file to 2000 PUMAs.
Additional resources that we provide include crosswalks between 2010 and 2020 PUMAs (through our 2020 PUMA page) and between 2000 and 2010 PUMAs (through our 2010 PUMA page); definitions for “ConsPUMAs” (sets of PUMAs that cover a consistent area over time) for two periods (2000-2010 PUMAs and 1980 county groups + 1990 & 2000 PUMAs); and GIS boundary files for all these entities (county groups, PUMAs, and ConsPUMAs), which you might use to determine spatial relationships among different PUMA definitions for which we don’t already provide a crosswalk.
We don’t have a resource that crosswalks across all these definitions, but you may be able to use these resources to develop such a crosswalk on your own or to achieve partial solutions.