you won't feel it shifting gears, there are no shifting of the gears in a cvt. it's a metal belt that moves along two different pulleys.
chances are your starter clutch is goin out, and no it's not like a clutch in a manual tranmission.
In essence the CVT "ranges" of CVT ratios, but the start clutch is used to engage and disengage the power between ranges. That's probably what you are feeling is the start clutch acting funny. I haven't figured out if mine has a worn start clutch or just the solenoid valve is gummed up or going bad and not providing enough positive pressure. The former is probably wishful thinking, and some of my holdover problem solving from more traditional auto transmissions in their higher mileage.
A more accurate post links back to this one with worse answers so I figured I should add my $0.02 worth after spending more than a few hours working on a basket case 2003 HCH1. Fun times.
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