As an Emmy-winning director on “The Sopranos,” “Mad Men” and “Game of Thrones,” Alan Taylor has made a name for himself on some of television’s most highly regarded series. Still, when he learned that he would be helming the most consequential action sequence in the history of “House of the Dragon,” he took a moment to consider the enormity of the task at hand. “I hadn’t really realized what a big deal it needed to be,” Taylor said.

Action set pieces rarely come bigger than the three-way dragon battle that concludes “The Red Dragon and the Gold,” the fourth episode of the fantasy series’ second season. A landmark event in “Fire & Blood,” author George R.R. Martin’s fictional history of the royal Targaryen clan that inspired the show, the so-called Dance of the Dragons sees a trio of fir

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