I think it would be wrong to imply
that everyone with the surname of SAPERIA and variants
necessarily belong to one family. Surnames in Russian controlled territories were only
made mandatory for Jews in 1821, before which they were just
known as X the son/daughter of Y. Before 1821 few families
would have had surnames as we know them except perhaps for
some rabbinic families - perhaps from the town where one of the
rabbinic forebears served or became famous.
Go to www.cindyslist.com/jewish.htm (this is a tremendous site for genealogical links) and click on the database of Jewish Surnames of the Russian Empire. Feed in 'sapir' and you will find three similar names (but not actually SAPERIA) either based on the Hebrew 'sapir' or the Yiddish 'shafir' (both meaning sapphire), or as a derivation of the name of the town Speyer in Germany.
The more likely explanation of the name SAPERIA is that it is derived from the Hebrew word SAPIR meaning 'sapphire'. In the regions of eastern Europe where they lived, surnames may not have been adopted (or imposed) until as late as the 1820's. If derived from Speyer in the Rhineland it would have necessitated the retention of some form of surname from as early as the 15th century, i.e.up to 400 years previously ! A name based on the Hebrew or Yiddish for sapphire would have been one of the so called 'ornamental' names adopted by families not necessarily related and possibly in widely dispersed places.
Most of the immigrants to Leeds, including the Saperia's, were Litvaks from Lithuania, north east Poland and parts of Belorussia and the Ukraine, where the Litvak dialect of Yiddish was spoken. Some Litvaks, like the Ephraimites of old, could not pronounce "sh" and hence Saperia might also be a form of the more common SHAPIRO, derived perhaps from non Litvak areas (but still probably based on the word Sapir).
Leeds has greatly changed and although there is still some industry here it is now a growing regional financial, legal and retail centre. The tailoring industry which once employed many thousands and in which the Jews were heavily involved (even in the 1920's 60% of Jewish bridegrooms listed 'tailor' as their occupation in the marriage registers) is now almost defunct. The Jewish community, like most provincial Jewish communities, it is now much reduced in size. From more than 20,000 at its peak in the 1920's it now numbers less than 8,000. I have found that the first mention of a SAPERIA in Leeds is in the 1871 census.