乘 vs 承 - are they related?
「乘」and「承」do indeed sound similar, but an etymological relation (if any) would be before the time of Old Chinese. They are unrelated, as far as usage or glyph origins is concerned.

乘
「乘」was originally a picture of a person「大」climbing on top of a tree「木」; feet「舛」were added on to the person later (Shape #2 onwards).
商甲粹1109合集6491西周金公臣簋集成4186篆說文解字　現代楷　
The original meanings were to ascend, to ride an object, extended to mean to take advantage of [a situation]. It does not mean to transfer, which is a coincidence due to its meaning of ride.

承
「承」was originally a picture of two hands「」and「又」holding up a kneeling person「卩」. The kneeling person's legs were straightened (Shape #2), then replaced with another hand「手」to emphasise the meaning of holding up, leaving behind a small shape representing the rest of the person (Shape #3 onwards).
商甲後2.30.12合集9175戰國金令狐君嗣子集成9719篆說文解字　現代楷　
The original meaning was to hold up, extended to mean to carry responsibility &gt; to inherit, carry on, continue. To transfer may give a wrong impression if used incorrectly; it is only related in the sense of to inherit, carry on, continue.

References:

季旭昇《說文新證》
小學堂
國學大師