To clarify, DBI takes care of saving the $sth. You don't have to worry about it. From the doc:

Like prepare except that the statement handle returned will be stored 
+in a hash associated with the $dbh. If another call is made to prepar
+e_cached with the same $statement and %attr values, then the correspo
+nding cached $sth will be returned without contacting the database se
+rver.
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So you go on about your business and let DBI worry the details.