According to one of these samples of public opinion, a swing of just 2% would give Yes the lead.
For those of us who support independence, these polls are obviously extremely encouraging. But with five months to go until referendum day - and with a significant number of people yet to make up their minds - there is absolutely no room for complacency.
The onus is still very much on the Yes campaign to persuade people of what we believe in our heads and in our hearts to be true - that we will be better off as an independent country.
However, a couple of things do strike me about the current state of play in the campaign.
The first is that people seem to be heartily sick of hearing the No campaign tell us what we can't do.
There is barely a day that passes without some dire prediction of what will happen if Scotland votes Yes.
Last week, we even had the UK Defence Secretary telling us that we will be more vulnerable to attacks from outer space if we become independent.
Does he really think people are stupid?
This week, Gordon Brown - the Chancellor whose pensions tax raid destroyed final salary pension schemes and who insulted pensioners with a 75p increase - will have the nerve to tell us our pensions won't be secure with independence.
The question he should be asked straight back is, why not?
After all, we already pay for our pensions - they are not some "gift" from Westminster.
Pensions will be guaranteed on independence - but more, importantly, independence will give us the chance to decide pensions policy for ourselves and make sure we can properly protect decent pensions for our older folk.
So, in my view, the negative, scaremongering approach of the No campaign is backfiring.
It insults people's intelligence and, by arrogantly suggesting that Westminster will call all the shots if we vote Yes, it is actually helping to make the case for independence.
But the second thing that strikes me is the more significant.
People are becoming more confident about our prospects as an independent country.
And why shouldn't we be? If Scotland was independent, we'd be the 14th richest country in the developed world.
The UK would be 18th. Many of the countries above us in that league table are small countries that share many similarities to Scotland.
So it is absurd to suggest that we couldn't be a successful, independent country.
We absolutely can be.
The big question we should be asking is how we make sure more of our citizens share in our wealth, rather than watching while Westminster policies push more people into poverty.
There is a long way to go in the referendum campaign. But at this stage there is plenty of evidence to suggest that it is hope and optimism that is winning.
And that's got to be a good thing.