ichidan verb
carry up; bring up
Used when physically moving something to a higher place, such as upstairs or onto a platform.
重い荷物を二階に運び上げる。
I carry the heavy luggage up to the second floor.
運ぶ is the general verb for carrying or transporting something, while 運び上げる specifically adds the direction of moving upward.
Compound of 運び (continuative form of 運ぶ, 'to carry') + 上げる ('to raise').