Can depression trigger manic episodes?

Not exactly: Depression and manic episodes can be part of the same disorder -- bipolar disorder. This is a problem with mood stability. One pole does not really trigger the other, but the person's mood may shift quickly back and forth. More commonly the shifts occur over longer time period, and there may be a time of relatively normal mood appearing before a manic episode.

Not quite: There is a natural rhythm to mania and depression, differing somewhat from person to person. But in the quest to avoid depressions, many manic-depressive peoour seek artificial highs (with drugs, for example) and some of these can trigger manic states--as well as being problematic in their own right. Sometimes the effect is well-intentioned: as when antidepressants trigger manic episodes.

Precede: I wouldn't say depression triggers mania; no one seems to know what actually does. However, I would say depression precedes mania. I guess the lesson here is that if we know a person is bipolar, and they happen to be in a depressed phase, that a manic phase can follow (but not trigger a manic episode) at any time.