OPEN UP! aku/akeru (開く & 開ける) vs. aku/akeru (空く & 空ける) vs. hiraku/hirakeru (開く & 開ける)

Someone recently asked about the difference between aku and hiraku, so here's my take on it, in case anyone else might find it useful (and if anyone finds any inaccuracies, please let me know):

Aku/hiraku are intransitive verbs for "to open" using the same kanji. The transitive counterparts are akeru/hirakeru.

I. AKU/AKERU (開く & 開ける)

I think of aku/akeru (開く & 開ける)　as referring to "making an opening" so there's a resulting hole or space. They are also used metaphorically for time expressions. So we can use it for doors, windows, bottles, cans, bags, boxes, eyes, mouths, time, etc.:

"mise ga aite-iru" = the store is open
"mise ga 9-ji ni akeru" = the store opens at 9:00
"mise o akete-iru" = (someone) is opening the store
"mado o aketara," = if you open the window,...
"kabe ni ana o aketa" = he made a hole in the wall
"doa ga aite-iru" = the door is open/ajar
"aita kuchi" = "open-mouthed" "agog"
"bin ga akanai" = I can't open the bottle
"me ga aite-inai" = his eyes are not open
"chakku ga aite-iru" = your fly is open

Hifana knows:

http://jp.youtube.com/watch?v=OIcG4X5g5FY

II. AKU/AKERU (空く & 空ける)

You can also use "aku/akeru" to mean "open" in the sense of vacant/free, but it's a different kanji, namely 空く & 空ける:

"kono seki ga aite-imasu ka?" = is this seat free?
"aite-inai heya" = an occupied room
"heya ga kanzen aite-imasen" = fully booked (hotel)
"ashita aite-imasu ka?" = are you free tomorrow?

III. HIRAKU/HIRAKERU (開く & 開ける)

In contrast, hiraku/hirakeru (開く & 開ける) is more like "to open up" so it's used for things with moving parts like umbrellas, and "to open out/wide/apart" in the sense of spreading things so for books, flowers, hands, (erm) legs, gates, shutters, collars. It's also used metaphorically for opening up your mind/heart/eyes. I've also noticed it being used for opening up computer files.

"mise o hiraku" = to open up (start) a business (cf. aku/akeru = to open for business)
"sensu o hiraku" = to open/unfold a fan
"kasa o hiraku" = to open an umbrella
"tsutsumi o hiraku to" = when you open the wrapping/parcel
"kyoukasho no 3 peeji o hiraite kudasai" = pls open to page 3 in your textbook
"mon wa hirakanai" = the gate won't open
"ashi o hiraite kudasai" = please spread your legs
"kaigi/tenrankai o hiraku" = to hold a meeting/exhibition"
"yatto kokoro o hiraite-imasu" = she's finally opening up to us
"shiten o hiraku tsumori desu" = they plan on opening up a branch office
"fairu o hiraku" = to open up a file
"sakura issei ni ga haita" = the cherries bloomed all at once

Did I miss/misstate anything?