It is illegal to move a nest with eggs or chicks in it. If you need to move the nest, you may need a permit.
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How to Tackle Bird Nest Removal - Bob Vila
Can You Legally Remove a Bird's Nest in the Hudson Valley?
NestWatch - Cornell Lab of Ornithology
When Is Bird Nest Removal OK? Wildlife Control and Exclusion
Bird nest blues: It's illegal to move a bird's nest – even if it's
Picking up baby birds can do more harm than good
VERIFY: Will birds abandon a nest touched by humans?
Will a mother bird come back if the nest is moved? - Quora