In the event of a big US price correction, will equities across the globe fall in tandem?

So, from what I can gather, in both 2000 and 2008 when the US market fell, that bled over globally, they all fell when the panic hit. It seems like in the event of big drawdowns, people pull cash from everywhere for liquidity, even if fundamentals aren't the same across the globe? After the initial drop, then the divergence happened in the recovery across different countries as some recovered much faster than others. Does this pattern hold for other historical corrections? Do you think it's l

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