The Faithful - S3-E4
Trivia: James and Winn find a meeting of Coville and his followers to be "a little cult-y." Melissa Benoist plays Rachel Koresh, the wife of cult leader David Koresh, in the miniseries Waco, a dramatization of the Waco siege - the 1993 standoff between the ATF and FBI and Koresh's Branch Davidians that lasted 51 days and resulted in 86 deaths.
In Search of Lost Time - S3-E15
Trivia: While Kara talks with Jònnz she mentions Jor el's phrase "The son becomes the father, the father becomes the son" that line was taken from Richard Donner's Superman the movie.
In Search of Lost Time - S3-E15
Trivia: While Kara is fighting the alien girl she takes a few pics in a photo booth, that's a small a reference to Superman IV.
Trivia: Erica Durance plays Melissa Benoist's mother in this episode. She played Lois Lane in the TV show Smallville, about Superman when he was young.
Trivia: The way Kara rejects the bullets from the machine gun is very similar to how Superman did in Superman Returns.
Answer: For one, it's usually cheaper to film in Vancouver because of the tax breaks. But all the CW Arrowverse shows (with the exception of "Black Lighting") are/were filmed in Vancouver. So it makes it easier and cheaper for sharing set designs, crossovers, etc ("Black Lightning" filmed in Vancouver during its crossover). Originally "Supergirl" wasn't part of the Arrowverse when it was on CBS, but it was too expensive to produce and wasn't reaching the wider audience the CW shows had. So CBS moved it to its sister company, The CW.
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