In the Reading Club series, we read books together, enjoy them, and learn from them.
Let’s read a bit of John le Carré‘s The Spy Who Came in From The Cold together.
Chapter 1: Checkpoint
PART 1
The American handed Leamas another cup of coffee and said, “Why don’t you go back and sleep? We can ring you if he shows up.”
Leamas said nothing, just stared through the window of the checkpoint, along the empty street.
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Well, I have just one question; to blow someone’s cover means to reveal their identity. I was wondering if blown meant exhausted here.
That’s an interesting point.
To the best of my knowledge, “blown” means “out of breath”. It could of course be interpreted as ‘exhausted” in certain contexts as you have mentioned.
However, in our context, I think the writer is trying to say:
His cover is blown, his true identity has been revealed, they know he is a spy, and therefore he is on the run, he is trying to escape.
I think you are right, I also found this meaning for blow as a verb:
23. (tr) slang to expose or betray (a person or thing meant to be kept secret)
And as an idiom:
4. blow one’s cover, to divulge one’s secret identity, esp. inadvertently.
To me, the first meaning fits better as it states that the man has been exposed.