Firework to rise rapidly (9)

I believe the answer is:

skyrocket

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'firework' is the definition.
(I know that skyrocket is a type of firework)

'to rise rapidly' is the wordplay.
'to' becomes 'sky' (I can't explain this - if you can you should believe this answer much more).
'rise rapidly' becomes 'rocket' (I've seen this in another clue).
'sky'+'rocket'='SKYROCKET'

Can you help me to learn more?

(Other definitions for skyrocket that I've seen before include "Increase very rapidly" , "Soar" , "Shoot up abruptly" , "Mushroom" , "Shoot up high" .)

I've seen this clue in The Irish Times.

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