Combine all ingredients (except celery salt) in a large bowl, stirring to mix thoroughly. Transfer mixture to a blender, working in batches if everything won't fit at once. Blend at high speed for 1 minute to thoroughly incorporate everything. Add celery salt and pulse blender briefly to combine. Strain through a fine mesh strainer, discarding solids (you can skip this step if you prefer more texture in your Bloody Mary.) Transfer to a glass bottle or other non-reactive airtight container and reserve in the refrigerator to chill thoroughly.
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