SuttaCentral
“Yā cāyaṃ, āvuso, appamāṇā cetovimutti, yā ca ākiñcaññā cetovimutti, yā ca suññatā cetovimutti, yā ca animittā cetovimutti—ime dhammā nānātthā ceva nānābyañjanā ca udāhu ekatthā byañjanameva nānan”ti?
MN 43
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Does both release through emptiness and signless refers to any specific state of jhana of the formless or arupa ? And cetovimutti is rightly translated as mind’s release or heart’s release ? Or both synonymous ?
Thank you
Analayo has related the different liberations to various types of satipatthana. I don’t offhand know of any relationship to the jhanas or arupas. 
Contemplating body and feeling leads to the desireless liberation, through the perception of dukkha.
Contemplating Mind leads to the emptiness liberation, through the perception of Anatta.
Contemplating dhammas leads to the signless liberation through the perception of Anicca.
{Edit : SA80 / MN121 has the proceedure for entering into the perception of emptiness and then taking it forwards.}
Cetovimutti can be loosely translated as the liberation of heart/mind/thought. The ancients believed the mind to be located in the region of the upper chest, where we now locate the heart.
“Release” is where the “non-emptiness” of the jhana is identified and release from it is attained:
"He discerns that ‘This theme-less concentration of awareness is fabricated & mentally fashioned.’ And he discerns that ‘Whatever is fabricated & mentally fashioned is inconstant & subject to cessation.’ For him — thus knowing, thus seeing — the mind is released from the effluent of sensuality, the effluent of becoming, the effluent of ignorance. With release, there is the knowledge, ‘Released.’ —MN 121
Deliverance of mind (ceto-vimutti) also refers to the boundless deliverance of the brahma-viharas. In its highest sense, deliverance of mind is linked with ‘deliverance through wisdom (panna-vimutti),’ which is the emptiness liberation. It can be seen that the emptiness release is described differently to the other two releases, in that it is an insight contemplation:
“And what is the emptiness awareness-release? There is the case where a monk, having gone into the wilderness, to the root of a tree, or into an empty dwelling, considers this: ‘This is empty of self or of anything pertaining to self.’[5] This is called the emptiness awareness-release.”—MN 43
This is a beautiful question, I appreciate you.
Animittā = Nirodha
The signless state is referring to state of Nirodha, it’s not referring to any state of Jhana. Decent to Nirodha can happen after neither perception nor perception state. Nirodha is a state where all perceptions/feelings/consciousness are ceased. It means there is no being there, only vitality of body functioning. It’s purest state. While one attains Sotapanna/Sakdhagami/Anagami this Nirodha state occurs for short period of time.
After one attains Anagami, a Anagami can enter into this state of Nirodha as many times as he wish. It’s possible only by Anagamis/Arahants. They will do a pre-determination to enter into that state, after that exact duration they will come out. There is a limit on duration one can be in Nirodha, it’s at most 7 days. If it’s more than 7 days the vitality of body disappears.
Suññatā = Nothingness (7th Jhana)
So, Animittā, Suññatā are different states.
There is an excellent discourse of this Sutta by Ven Bhante Vimalaramsi. Highly recommend to go through it, its worth.
MN 43 The Greater Series of Questions and Answers
p.s. Many of his students easily experience different levels of Jhana. And I heard some of his students enter to Nirodha
Finally a quote, the understanding comes only by experience.
Regarding emptiness, signless, or cetovimutti, you may read pp. 51-64 in The Notion of Emptiness in Early Buddhism by Choong Mun-keat.