I want to cross over the river.
I want to cross the river.
Which one of the sentences conveys correct meaning?
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Both are perfectly good. "Cross the river" is much more common, (3709 hits in the iWeb corpus, against 144 for "cross over the river").
To me "cross over the river" puts emphasis on the process of actually crossing, whereas "cross the river" is usually about getting to somewhere on the other side.