When I first started reading poetry I approached it as I would a novel - thinking I had to read one collection at a time from cover to cover, then I began dipping in and out. Now I read cover to cover but I may well have several collections on the go at any given time. Take today for instance, I read a pamphlet sized collection cover to cover and made notes on it for an endorsement I am writing, but I have also dipped into several other collections I am reading, as well as reading bits of a journal and reading some poems online. This seems to me a very natural way of reading. It is rare that a poetry collection is so riveting that I can't put it down and have to compulsively read it straight through - although it does happen (and is a treat when it does) and some poetry collections take a great deal of concentration and mental processing - in these cases I can only read a few pages at a time before I need to take a break. Using my old mode of poetry reading I would have probably put the book down after those few pages and gone and found something else to do or read a novel. Now, if I choose to, I can move onto reading a different collection.
I seem to have developed this mercurial mind approach to reading in general. I still tend only to read one novel at a time (although I may have several I have started and stopped and might later come back to) but I will also have several poetry collections, a short story collection or two and several non fiction books on the go at any given time. In fact Goodreads tells me that I am currently reading 36 books. I think I developed this way of reading when I was studying - I like it it means I spend more time reading overall and that I read more books - something that feels more urgent as you get older. and feel you might be running out of time.
I don't do massively close readings of every poetry collection I read. I usually give more attention to the books I find more engaging. Collections where I want to come back to particular poems again and again. With these collections I sometimes make notes or post snippets on Twitter so that I can remember them later - and perhaps to entice other readers to seek out the book. If I am not finding a collection engaging or am finding it difficult I don't usually give up. Often I will try reading poems several times or reading them aloud to see if I can make more sense of them or get a feel for them. Sometimes I put the book away on a to read pile so that I can come back to it later - it might simply be that I am not in the right frame of mind for it - after all we bring all our emotional states and baggage to a reading of any book. There are, of course, books I don't love. These tend to be discarded after reading - these could be mediocre writing, but they can also be books that I am simply not ready for yet. I remember reading a few books when I did my degree and hating them - Ted Hughes Crow was one of them - I loathed it - I found the language ugly and heavy and too masculine. However a couple of years later I suddenly had a hankering to read it and this time I loved it - it was all those things of course but now I "got it." I think I simply wasn't ready for it yet the first time I was introduced to it. I think of it as a kind of reading evolution. It's like studying art - most people don't love abstract without first gaining an appreciation of more conventional forms - it's like you work your way up to abstract through studying the history of art so that when you get there you can fully appreciate it. Poetry is the same I think - one starts with the more conventional and works one's way towards an appreciation of the more surreal and experimental.