continue:后一个动作接着之前的动作,接doing表示前后动作相同,接to do表示前一个动作已完成。例如,I continue sleeping(之前也在睡觉). After reading,I continue to sleep(之前在读书)。
carry on(with)后面要接名词(有坚持的意思),Ignoring their objection, I carry on with my experiment.
go on (with)后面接名词,在表示继续做之前在做的事情。 Go on with your homework。
keep up with:保持,赶上的意思,I tried to keep up with you.
keep on with:持续某种状态,反复做,Don‘t keep on complaining. The rain kept on all night.