We don't have synonyms for asman yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are asian, atman and Asian.
(n) :
(Zoroastrianism) Avestan and Middle Persian name of the Zoroastrian divinity that is the hypostasis of the sky. Asman is the "highest heaven," and is distinguished from the firmament, 𐬚𐬡𐬁𐬴𐬀 (θβāṣ̌a), which lies nearer the earth.
(n) :
(Zoroastrianism) Avestan and Middle Persian name of the Zoroastrian divinity that is the hypostasis of the sky. Asman is the "highest heaven," and is distinguished from the firmament, 𐬚𐬡𐬁𐬴𐬀 (θβāṣ̌a), which lies nearer the earth.