Your request can be rewritten using the aliases of the nested subqueries. This should work for you:
SELECT u.* FROM (
(SELECT s1.title, s1.relavency, 'search1' as source FROM search1 AS s1
ORDER BY s1.relavency DESC
LIMIT 10)
UNION
(SELECT s2.title, s2.relavency, 'search2' as source FROM search2 AS s2
ORDER BY s2.relavency DESC
LIMIT 10)
) AS u ORDER BY u.relavency DESC
LIMIT 10
FYI: "", , .