Flat inside in two directions but swells (8)

I believe the answer is:

inflates

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'swells' is the definition.
The answer and definition can be both related to change as well as being verbs in their -s form.
Maybe they are linked in a way I don't understand?

'flat inside in two directions' is the wordplay.
'two directions' can mean two substitutions for 'direction'.
'inside' means one lot of letters goes inside another.
'direction' becomes 'e' (E is an example).
'direction' becomes 's' (S is an example).
'in'+'e'='ine'
'flat' going inside 'ine' is 'inflate'.
'inflate'+'s'='INFLATES'

'but' is the link.

Can you help me to learn more?

(Other definitions for inflates that I've seen before include "Blows up" , "Exaggerates" .)

I've seen this clue in the Sydney Morning Herald.

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