Equity relates to quantity, for instance capital distributed in equal units; Equality relates to distribution for instance distribution of income equally; Fairness relates to accountability and transparency, for instance fair economic policy
Since the topics listed here are tied to economic develoment, poverty reduction, and community governance I would add that "equity" can also refer to social assets that have been built over time. A persons (or an institutions) reputation, prestige, or standing in the community are tremendously valuable here. All are sought, one way or another, in communities at all levels.
Viewed this way "equality" does relate to distribution, but is tied to the distribution of opportunities. If opportunities aren't fairly distributed or are not made widely available economic development and poverty reduction are in trouble. Tying the two concepts together help us see that it's very difficult to build equity (social assets) in a community if equality of opportunities are not distributed fairly, or shut down.
This is where "fairness" comes into play, which Dr. Arjun Pangannavar's references to accountability and transparency aptly capture.
In Indian political context, according to Constitution of India, 'Equity' means 'all are equal before law' and justice means equal distribution of income, wealth and opportunities. Fairness means unbiased
Equality is about treating people similarly - giving them equal opportunity. Equity is about treating differently people differently so that there is equitable outcomes. Equity is about fairness. A good story to illustrate this is a thirsty fox and crane being given a saucer of water each to drink. Only the fox can drink (equality approach). The crane needs a beaker to drink as its structure/needs are different (equity approach). Fairness can only be achieved through this approach- quench the thirst of both foxes and cranes. This requires not only taking differentiated needs into account, but putting ceilings on the rich. If they have 3 houses in India, the price of land goes up and the poor cannot buy one! Thus it is a zero sum game- redistribution is necessary for fairness.
I would use Konow (2003) Which Is the Fairest One of All?
A Positive Analysis of Justice Theories. Journal of Economic Literature XLI pp. 1188–1239.
The article gives detailed overview of fairness concept (justice).
Here are some citations:
"...elements of justice inspire four corresponding theoretical categories (or families) into which each of the theories is placed and analyzed." p. 1189
The category equality and need
The category utilitarianism and welfare economics
The category equity and desert
The category family
"In social psychology, one of the leading pluralistic approaches is that of Morton Deutsch (1985), who proposes three principles, viz., equality, equity (or proportionality) and need, which in his scheme are specific to different contexts." p. 1232