All three forms of spirit are called "breath".
Our soul breathes in the spirit that is exhaled by God; the Holy Spirit that emmanates from God.
The ruach (spirit) of God has made me, and the breath (neshama; Spirit) of the Almighty gives me life. Job 33:4
In whose hand is the nephesh (soul) of every living thing, the breath (ruach; spirit) of all mankind. Job 12:10
(and about Leviathan) His breath (Nephesh; soul) kindles coals, and a flame comes forth from his mouth. Job 41:21
The breath of the Leviathan is the animal soul; the life-force that inhabits all living beings.
The same word for spirit, Ruach is used to indicate the lifeforce, Prana or Chi of all living beings as well as the Holy Spirit of God.
It is the spirit (ruach) in a man, the breath (neshama; Spirit) of the Almighty, that makes him understand. Job 32:8
They went with Noah into the ark, two and two of all flesh in which is the breath (Ruach) of life. Ge 7:15