Fetching details from the dictionary...
to fly about; to flutter about; to flit about; to fly past each other
春になると蝶が庭を飛び交う。
When spring comes, butterflies flutter about the garden.
記者会見では質問が飛び交っていた。
Questions were flying back and forth at the press conference.
SNSでうわさが飛び交ったが事実ではなかった。
Rumors flew around on social media, but they weren't true.