Anthropic is taking a big step toward a blockbuster stock listing that would rank among the biggest IPOs ever. Patrick Sison/AP Photo hide caption

Patrick Sison/AP Photo

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The artificial intelligence startup Anthropic, maker of the hugely popular Claude AI models, has taken a major step toward holding an initial public offering that analysts expect to be one of the biggest ever.

Anthropic filed final paperwork with regulators on Monday for an IPO under the ticker symbol ANT that reports have said could value the company at between $1.5 trillion and $2 trillion .

That would put it in league with Elon Musk's rocketry and AI company SpaceX, which was valued at around $1.8 trillion when it listed in June .…