It's hard to give you a completely accurate answer without knowing the type of item you're asking about nor the nature of its attunement. However, if I were to give a quick compact answer it would be:
Blink can transport the items you are carrying as long as they obey the following conditions: The item is not cursed, is currently within the 5 square block you're occupying and not exceeding twice your height, you are the only one carrying that item, and you're not pushing near the limits of your carrying capacity.
By that, I mean that like Szega said, and as you read, though the spell doesn't mention the items you're carrying or have equipped, it would be odd for the spell not to include them. The only valid reason I could think of as to why the spell is omitting that part has to do with the prior conditions.
Though attunement relates to your ability to wield the item, and not your ability to carry it I do remember a campaign where our druid took the staff belonging to the cult leader we had just vanquished. That staff happened to be cursed and sentient and chose to attune itself to our druid. Though it gave him a few benefits, there were just as many quirks. For instance, due to its sentience, it had the ability to decide what consisted of wielding it and would harm whoever grabbed it even in an attempt to give it to our druid. Another ability it had was to jump into the druid's hand on command from 30 feet away. So for this reason, I'd avoid touching cursed items from your teammates.
Occupying Space and Semi-Control
This, I believe is the most logical and base reason to avoid putting objects in the spell's description. While dealing with an item, there are many players who will try to push the limits on how much you can carry. For instance, say the item in question is a grappling hook you had just hooked onto an eagle. Then are you carrying the eagle? If an enemy has a hold of your spear, then does the half he's holding break off?
Though my numbers are a bit arbitrary, the idea I was pointing out was to say that the only way to avoid such nonsensical arguments is to keep in mind that you must be holding it close to you (so no extended trick with a rope.)
This one is more of a safety net than anything else. The spell states you are taken to an Ethereal Realm and doesn't mention things like time, or if it's the same space. Keeping this in mind, avoiding any chance of dropping the item while in travel would be beneficial.