at least one member of a list within another list when querying over a join
SELECT DISTINCT
   a.id,
   a.etc
FROM years y
JOIN activitymapper am
   ON (y.targetyearid = am.targetyearid)
JOIN activity a
   ON (a.id = am.activityid)
WHERE y.targetyearname IN ('Year1', 'Year2')


Should do it. We're going from years to activity through activitymapper, selecting each activity only once (DISTINCT).