Hi,Hannah We soldem use the expression"给过去" but "递过去". As a matter of fact,there is no great difference between "递"and"给" if you regard them as verbs.What's more,there exists a phrase "递给" which has the similar meaning of "递" and "给".But "给"is used more often.You can remember some regular collocations suah as "递文件" and "给你". Addtionally,"给" can be a preposition which means to.For example,"给/致爱丽丝"equels to To Alice. If my answer make you confused,please don't hesitate to ask me.I will be there to help you.

递 pay attention to the process.(pass) 给 pay attention to the result.(give)

我递雨伞给你。 I pass on umbrella to you. 我给你一把雨伞。 I give you an umbrella.

Really good question，But this question is so difficult for me to answer in English, “递过去” == “ 给过去” ==“ 拿过去”，we use "给你”，we don't use "递你" We use "快递” We don't use "快给“。Do you understand ?