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Common Stock - Additional Information (Detail) - $ / shares	Dec. 31, 2024	Sep. 30, 2024	Sep. 30, 2023
Stockholders' Equity Note [Abstract]
Warrants of common stock exercise price	$ 3.98
Common stock, warrants issued	4,899,497	4,899,497	4,899,497
Common stock, warrants outstanding	4,899,497	4,899,497	4,899,497

X

- Definition

Class of warrants or right issued.

+ References

No definition available.

+ Details

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Namespace Prefix:	mesa_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

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X

- Definition

Number of warrants or rights outstanding.

+ References

No definition available.

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- References

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